Area of Circle Exercises
Area of a circle practice problems with answers.
There are twelve (12) practice problems in this exercise about the area of the circle . You may use a calculator. Do not round intermediate calculations.
Round your final answer to two decimal places unless the exact answer is required.
For your convenience, I have included the different variations of formulas that you can use to find the area of a circle.
Problem 1: What is the area of a circle with radius [latex]8[/latex] meters? Leave your answer in terms of [latex]\large{\pi}[/latex].
This problem requires us to leave our answer in terms of [latex]\pi[/latex].
[latex]64\pi [/latex] square meters
Problem 2: The diameter of a circle is [latex]4.5[/latex] feet. Find its area. Use [latex]\pi = 3.1416[/latex].
[latex]15.90[/latex] square feet
Problem 3: Find the area of the circle below with a given radius. Use [latex]\pi = 3.14[/latex]
[latex]907.46[/latex] square centimeters
Problem 4: Find the area of the circle below with a given diameter. Use the value of [latex]\pi[/latex] on your calculator.
Make sure that you use the internal value of [latex]\pi[/latex] on your calculator.
[latex]60.00[/latex] square inches
Problem 5: The circumference of a circle is [latex]22.2[/latex] feet. What is its area? Use [latex]\pi = 3.14[/latex]
[latex]39.24[/latex] square feet
Problem 6: Determine the area of a dinner plate with a circumference of [latex]37.68[/latex] inches. Use [latex]\pi = 3.14[/latex].
[latex]113.04[/latex] square inches
Problem 7: The radius of a circle is [latex]5[/latex] inches. Find the area of the circle expressed in square centimeters [latex]c{m^2}[/latex]. Use 1 in = 2.54 cm. Use [latex]\pi = 3.14[/latex].
Convert [latex]5[/latex] inches to centimeters.
The area is
[latex]506.45[/latex] square centimeters
Problem 8: The diameter of a circle is [latex]12.4[/latex] miles. Calculate the area of the circle in terms of square kilometers [latex]k{m^2}[/latex]. Use 1 mi = 1.609 km. Use [latex]\pi = 3.1416[/latex].
Convert [latex]12.4[/latex] miles to kilometers.
[latex]312.64[/latex] square kilometers
Problem 9: What is the radius of a circle with an area of [latex]73.12[/latex] square miles [latex]m{i^2}[/latex]? Use [latex]\large{\pi = {{22} \over 7}}[/latex].
[latex]4.82[/latex] miles
Problem 10: Determine the diameter of the circle having an area of [latex]100[/latex] square yards [latex]y{d^2}[/latex]. Use [latex]\large{\pi = {{22} \over 7}}[/latex].
[latex]11.28[/latex] miles
Problem 11: Find the area of the semicircle below with a diameter of [latex]8[/latex] centimeters. Use [latex]\pi = 3.1416[/latex].
The area of a semicircle is half of the area of a circle.
[latex]27.33[/latex] square centimeters
Problem 12: Both circles share the same center. Find the exact area of the shaded region.
Area of the shaded region = area of the larger circle minus area of the smaller (inner) circle
[latex]21\pi [/latex] square inches
You may also be interested in these related math lessons or tutorials:
Area of a Circle
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Course: 7th grade > Unit 9
- Finding circumference of a circle when given the area
- Area of a shaded region
- Impact of increasing the radius
- Circumference and rotations
Area and circumference of circles challenge
- Shaded areas
- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi
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Area of a Circle Support Page
Welcome to our Area of a Circle page. Here you will find a range of free printable area sheets and support, which will help your child to learn to work out the area of different circles.
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Area of a Circle
On this webpage you will find our range of worksheets to help your child learn to work out the area of a range of circles.
These sheets are graded from easiest to hardest, and each sheet comes complete with answers.
Using these sheets will help your child to:
- understand what area is;
- know how to find the area of a circle;
- solve word problems involving area of circles;
Want to test yourself to see how well you have understood this skill?.
- Try our NEW quick quiz at the bottom of this page.
Quicklinks to ...
- What is area?
How to find the Area of a Circle
- Area of a Circle Calculator
Area of a Circle Worksheets
Area of a circle word problems.
- More recommended resources
Area of a Circle Online Quiz
What is area.
- Area is a measure of the amount of space inside a shape.
- It is measured in squares, so it can be square inches (in 2 ), square cm (cm 2 ), square feet(ft 2 ), etc.
The formula for the area of a circle is: A = πr 2 , where r is the radius of the circle.
To find the area of a circle, follow these simple steps:
- find the radius of the circle (the distance from one side to the center of the circle). It is the same as half of the diameter of the circle.
- square the radius (multiply the radius by itself)
- multiply this amount by pi (π)
- you have now found the area of the circle.
- the formula for the circumference of a circle is A = π x r x r or A = π r 2 , where A is the area and r is the radius of the circle.
Pi (written π) is a special mathematical number which is used to help calculate areas and perimeters of circles.
Pi always has the same value which is 3.141592...
Area of a Circle Examples
Area of a circle example 1.
Find the area of the circle below to 1 decimal place.
To find the area of the circle, we need to find the radius first.
The radius is half of the diameter, so it is half of 5 = 2.5 cm.
Next we need to square the radius: 2.5 2 = 2.5 x 2.5 = 6.25 cm.
Finally we need to multiply this amount by pi (π).
So the area of this circle is π x r 2 = π x 6.25 cm.
If we take pi = 3.14, this gives us an area of 3.14 x 6.25 = 19.6 square cm or 19.6 cm 2 to 1 decimal place.
Area of a Circle Example 2
Find the area of the circle below to the nearest inch.
To find the area of a circle, we need to find the radius first.
The radius of the circle is half of the diamter which is half of 7 = 3.5 inches.
Next we need to square the radius: 3.5 2 = 3.5 x 3.5 = 12.25 cm.
So the area of this circle is π x r 2 = π x 12.25 cm.
If we take pi = 3.14, this gives us an area of 3.14 x 12.25 = 38.5 square inches or 38.5 in 2 to 1 decimal place.
Area of a Circle Example 3
Find the area of the circle below and give your answer to the nearest whole number.
To find the area of a circle, we need to square the radius and multiply this by pi (π)
The radius of the circle is 12m, so the square of the radius is 12 2 = 12 x 12 = 144.
So the area of this circle is π x r 2 = π x 144 m.
This gives us an area of π x 144 = 452 square m or 452 m 2 to the nearest whole number.
Our Area of a Circle Calculator will find the area of any circle, if you type in a radius or diameter.
It will take whole numbers, fractions or decimal values.
The best thing about it is that it shows the working out, step-by-step.
We have split the worksheets into 2 different sections:
- This section contains straightforward area of circle questions;
- Each worksheet comes with two versions: version A is in standard units, version B is in metric units.
Sheets 1A and 1B contain circles with the radius marked.
Sheets 2A and 2B contain circles with the diameter marked.
Sheets 3A and 3B contain a mixture of circles with either the diameter or the radius marked.
- Area of a Circle Sheet 1A
- PDF version
- Area of a Circle Sheet 1B (metric version)
- Area of a Circle Sheet 2A
- Area of a Circle Sheet 2B (metric version)
- Area of a Circle Sheet 3A
- Area of a Circle Sheet 3B (metric version)
Sheets 1A and 1B contain straightforward area word problems.
Sheets 2A and 2B contain slightly harder word problems.
Sheets 3A and 3B are the hardest sheets and require multiple steps involving subtracting the areas of circles to find the areas of more complex shapes.
- Area of a Circle Word Problems 1A
- Area of a Circle Word Problems 1B (metric version)
- Area of a Circle Word Problems 2A
- Area of a Circle Word Problems 2B (metric version)
- Area of a Circle Word Problems 3A (harder)
- Area of a Circle Word Problems 3B (harder - metric version)
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
More Circle Worksheets
- Area of a Semi-Circle
- Area of 1/4 Circle Support
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- Square Inside a Circle Area Support Page
- Perimeter of a Circle
- Perimeter of a Semi-Circle
More Area Support and Resources
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In order to access this I need to be confident with:
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This topic is relevant for:
Area Of A Circle
Here we will learn about calculating the area of a circle including how to calculate the area of a circle given the radius, how to calculate the area of a circle given the diameter and how to calculate the area of a circle given the circumference.
There are also area of a circle worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What is the area of a circle?
The area of a circle is given by the area of a circle formula which is made by using a specific relationship between the radius of a circle and its area.
Area of a circle formula:
we usually simplify this to
E.g. What is the area of a circle with radius 3cm ?
What is pi?
\pi (pronounced pi) represents the ratio of the circumference of a circle to its diameter. For all circles if you divide the length of the circumference by the length of the diameter you get the value \pi .
Note : \pi is an irrational number which means it cannot be written as a fraction. It is a non recurring decimal and has an approximate value of 3.14159…
In GCSE you should use the \pi button on your Casio calculator when working with \pi . To get this you need to press [SHIFT][ \times 10^x ]. Alternatively you can use the value 3.142 instead.
Sometimes a question may ask you to leave an answer in terms of pi E.g 6 \times \pi = 6\pi (this is an answer in terms of pi)
8 \times \pi = 8\pi (this is an answer in terms of pi)
10 \times \pi = 31.41... (this is an answer not in terms of pi)
How to calculate the area of a circle
In order to calculate the area of a circle:
Find the radius of the circle.
- Use the formula \text{Area of a circle} = \pi r^2 to calculate the area of the circle.
Give your answer clearly with the correct units.
Explain how to calculate the area of a circle
Area of a circle worksheet
Get your free area of a circle worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Area of a circle examples
Example 1: calculating the area of the circle given the radius.
A circle has a radius of 6cm , calculate its area. Give your answer to 2dp .
The radius is given in the question
Radius =6cm
2 Use the formula \pi r^2 to calculate the area of the circle.
3 Give your answer clearly with the correct units.
Remember the question asks you to round your answer to ‘2 decimal places’
Example 2: calculating the area of the circle given the diameter
A circle has a diameter of 10mm. , calculate its area. Give your answer to 1dp .
In this question the question gives you the diameter. You need the radius to find the area of the circle.
Remember the diameter of the circle is twice the radius.
Diameter = 10mm
Radius =10mm \div 2
Radius = 5mm
Use the formula \pi r^2 to calculate the area of the circle.
Remember the question asks you to round your answer to ‘1 decimal place’
Example 3: calculating the area of the circle, given the radius, answer in terms of 𝝅
A circle has a radius of 8m. , calculate its area. Give your answer in terms of \pi .
Radius = 8m
Remember the question asks you to give your answer to ‘in terms of \pi .
Example 4: calculating the area of the circle given the diameter
A circle has a diameter of 420km. , calculate its area. Give your answer in terms of \pi
Diameter = 420km
Radius = 420km \div 2
Radius = 210km
You leave the answer in the form 44100 \pi
Example 5: calculating the area of the circle given the circumference of a circle
A circle has a circumference of 21cm , calculate its area. Give your answer to 2dp .
The question gives you the circumference of the circle. But you need the radius
You know that the circumference of a circle is equal to 2\pi r
This means you can find the radius of the circle from the circumference, see below:
Circumference = 2\pi r
Circumference = 21
21 = 2\pi r
Divide both sides by 2\pi
\frac{21}{2\pi}= r
Notice how we leave our answer in terms of \pi at this stage. This is so you do not cause a rounding error later on in the question.
Remember the question asks you to round your answer to ‘2 decimal place’
Example 6: calculating the area of a semi-circle given the diameter
A semicircle has a diameter of 20m. , calculate its area.
Give your answer in terms of \pi
Diameter = 20m
Radius = 20m \div 2
Radius = 10m
This represents the area of a whole circle with a diameter of 20m. A semi circle has half the area of a full circle so you need to divide your answer by two. Remember to keep it in terms of \pi .
\begin{aligned} &100\pi \div2 \\\\ &50\pi \end{aligned}
Common misconceptions
You must have the radius to find the area of a circle by using the formula. If a question does not give the radius directly then it must be calculated.
- Correct units
When working with area you must always give the correct units squared E.g. cm^2 , m^2, km^2 etc.
It is important to only round at the end of the question and ensure you are round to what the question specifies. E.g. to 2 decimal places
- I n terms of \pi
Sometimes the question may ask you to give the answer in terms of \pi ’. This means you do not give the numerical answer that is produced when you multiply it by \pi
6 x \pi = 6 \pi (this is an answer in terms of pi)
6 x \pi = 18.8495592… (this answer is not in terms of pi)
- Misuse of calculator
Ensure you know how to correctly use the \pi button on your calculator.
Practice area of a circle questions
1. A circle has a diameter of 6cm . What is the radius of the circle?
The diameter of the circle is twice the size of the radius. Therefore to find the radius you can divide the diameter by 2.
2. Which of these answers is in terms of \pi ?
10 \pi means 10 lots of \pi
3. A circle has a radius of 1cm. What is its area to 1 decimal place?
Area of a circle = \pi r^2
\pi \times 1 \times 1 is equal to 3.1415…
This answer is correctly rounded to 1 decimal place and has the correct units.
4. A circle has a radius of 1cm. What is its area in terms of \pi ?
\pi \times 1 \times 1 is equal to \pi
This answer is correctly given in terms of \pi and has the correct units.
5. A circle has a diameter of 2cm. What is its area in terms of \pi ?
You must first divide the diameter by 2 to find the radius, 2cm divided by 2 is equal to 1cm.
Therefore the radius is 1cm
6. A circle has a diameter of 100cm. What is its area to the nearest whole number?
\pi \times 100 \times 100 is equal to 31415.92654…
Which is 31416 cm^2 rounded to the nearest whole number.
Area of a circle GCSE questions
1. The radius of a circle is 3.5 cm . Work out the area of the circle. Give your answer correct to 3 significant figures.
\pi \times3.5\times 3.5 or 38.4845… seen
2. The radius of a circle is 17.2 m . Work out the area of the circle. Give your answer correct to 2 decimal places.
\pi \times17.2\times 17.2 or 929.408… seen
3. The diameter of a circle is 20mm . Work out the area of the circle. Give your answer in terms of \pi .
4. The diameter of a circle is 15cm . Work out the area of the circle. Give your answer to 1 decimal place.
176.7 (1.d.p)
5. The circumference of a circle is 72cm . Work out the area of the circle. Give your answer correct to the nearest integer.
\frac{72}{2\pi}= r or \frac{36}{\pi}= r seen
412.52961… seen
6. A tile is in the shape of a semicircle. The perimeter of a semi circle is 12.85cm and the length of the arc is 7.85cm . Work out the total area of the tile. Give your answer correct to the nearest integer.
Length of diameter = 5cm
6.25\pi or 19.634… seen
“19.634…” ÷ 2 or 9.817… seen
7. The area of a circle is 64\pi cm^2 . Calculate the radius of the circle.
Only positive value should be given
Learning checklist
You have now learned how to:
- Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference
- Know the formulae for area of a circle
- Give answers in terms of \pi
- Calculate area of 2D shapes including circles and semi-circles
The next lessons are
- Circumference of a circle
- Arc lengths
- Area of a sector
- Perimeter of a sector
- Circle graph
- Equation of a circle
- Circle theorems
- Surface area and volume of spheres
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Circles Mixed Exercises
Area, circumference, diameter and radius
Area and circumference both relate to the radius and diameter of a circle. Once you know one, you can find all of the others -- It just takes a little math!
Practice Problems
If a circle's diameter is 10, calculate its circumference and area ?
Circumference = Π×diameter = 10 Π
radius = diameter ÷ 2 = 10 ÷ 2 = 5
A circle's area is 16Π. What is its circumference ?
Circumference = 2Π × radius = 2Π × 4 = 8Π
If a circle has a circumference of 26Π, what is its area .
Area = Π(radius)² = Π(13)² = 169Π
Interesting Fact about Circumference and Area
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- Problems On Circles
Problems On Area And Circumference Of A Circle
Before looking at problems on a circle based on perimeter and area, we need to understand the meaning of a circle and both the properties of the circle. In geometry, a circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the centre. Let’s have a look the definitions of perimeter and area given below:
Perimeter Definition
Perimeter is associated with any closed figure like triangle , quadrilateral, polygons or circles. It is the measure of distance covered while going around the closed figure on its boundary.
For example, the perimeter of a square of side 2 cm = 8 cm, as we know that the square comprises 4 sides having equal lengths, thus the total distance covered will be 4×2, which will be the total length (i.e. perimeter).
Area Definition
Area means the actual space enclosed by a closed figure (or within the perimeter), and it means all the points within the closed figure and not the boundary.
Perimeter and Area of Circle Formula
Now, coming to the perimeter of a circle, as explained above, is the measure of distance going around the circle’s boundary. This distance is difficult to calculate precisely, and it is easy to visualize that the distance to go around is larger in a larger radius than a smaller radius. Hence, the perimeter is a function of the radius of a circle. In the case of the circle, we generally use the term “CIRCUMFERENCE” instead of the perimeter.
It is given by,
Circumference = 2πr
Here, r is a radius, and π is a constant defined as the ratio of circumference to the circle’s diameter.
The value of π is 22/7 or 3.1416
Also check: Circumference of a circle
The formula to find the area of a circle is given as:
Solved Problems on Circle
Let us understand the concepts related to circles along with the following questions-
To cover a distance of 10 km, a wheel rotates 5000 times. Find the radius of the wheel.
Number of rotations = 5000.
Total distance covered = 10 km
Let ‘r’ be the radius of the wheel.
Circumference of the wheel = Distance covered in 1 rotation = 2πr.
In 5000 rotations, the distance covered = 10 km = 1000000 cm.
\(\begin{array}{l}\text{Hence, in 1 rotation, the distance covered = }\frac{1000000}{5000}cm=200\: cm\end{array} \)
But this is equal to the circumference. Hence, 2πr = 200 cm
Taking the approximate value of π as 22/7, we get
r = 100 x 7/22
r = 31.82 cm approx.
The diameter of a semicircular shape is 14 cm. What will be the perimeter of this shape?
Diameter of semicircle = d = 14 cm
Radius = r = d/2 = 14/2 = 7 cm
Perimeter of semicircle = (Perimeter of circle/2) + d
= (2πr/2) + d
= (22/7) × 7 + 14
The difference between the circumference and the diameter of a circular bangle is 5 cm. Find the radius of the bangle. (Take π = 22/7)
Solution: Let the radius of the bangle be ’r’
According to the question:
Circumference – Diameter=5 cm
We know, Circumference of a circle = 2πr
Diameter of a circle = 2r
Therefore, 2πr – 2r =5 cm
2r(π-1) = 5 cm
\(\begin{array}{l}2r(\frac{22}{7}-1)=5cm\\ \\ 2r\times \frac{15}{7}=5\\ \\ r=\frac{5\times 7}{15\times 2}\\ \\ r=1.166cm\end{array} \)
The radius of bangle is 1.166 cm.
A girl wants to make a square-shaped figure from a circular wire of radius 49 cm. Determine the sides of a square.
Solution: Let the radius of the circle be ’r’.
Length of the wire=circumference of the circle= 2πr
\(\begin{array}{l}= 2\times \frac{22}{7}\times 49=2\times 22\times 7\\ \\ =308\: cm\end{array} \)
Let the side of the square be ‘s’.
Perimeter of the square = length of the wire = 4s
\(\begin{array}{l}s=\frac{308}{4}\\ \\ s=77\:cm\end{array} \)
Therefore, the sides of the square is 77 cm.
Find the area of a circular region whose radius is 21 m.
Radius of circular region = r = 21 m
Area of a circle = πr 2
= (22/7) × 21 × 21
= 22 × 3 × 21
= 1386 sq. m
Therefore, the area of the circular region is 1386 sq. m.
Video Lessons on Circles
Introduction to circles.
Parts of a Circle
Area of a Circle
All about Circles
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| → → Circle This generator makes worksheets for calculating the radius, diameter, circumference, or area of a circle, when one of those is given (either radius, diameter, circumference, or area is given). They can be made in PDF or html formats. Options are numerous: you can choose metric or customary units or both, you can include or not include simple circle images in the problems, or randomly let some problems have a circle image and some not. You can also choose either 3.14 or 3.1416 as a value of Pi in the calculations, and then choose the rounding accuracy for the answers. Please change the different options to see what their effect is. After you have generated a worksheet, you can just refresh the page from your browser window (or hit F5) to get another worksheet with different problems but using the same options. All worksheets come with an answer key. You can print the worksheet directly from your browser, or save it on disk using the "Save as" command of your browser. If the problems on the worksheet don't fit the page or there is not enough working space, choose a smaller font, less cellpadding, or fewer columns of problems.
 Key to Geometry WorkbooksHere is a non-intimidating way to prepare students for formal geometry. Key to Geometry workbooks introduce students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps-and are prompted to form their own generalizations. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Circle Problems - Radius, Diameter, Circumference and AreaRelated Topics & Worksheets: Circles Circumference Of Circle Area Of Circle Objective: I know how to calculate problems that involve the radius, diameter, circumference and area of circle. The circumference of a circle is the distance around the circle. The formula is π d or 2π r Read the lesson on circumference of circle if you need to learn how to calculate the circumference of a circle. The area of a circle is size of the surface of the circle. The formula is π r 2 . The area of the circle is expressed in square units. Since the formula is only given in terms of radius, remember to change from diameter to radius when necessary. Read the lesson on area of circle if you need to learn how to calculate the area of a circle.  We hope that the free math worksheets have been helpful. We encourage parents and teachers to select the topics according to the needs of the child. For more difficult questions, the child may be encouraged to work out the problem on a piece of paper before entering the solution. We hope that the kids will also love the fun stuff and puzzles. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
 Area of a Circle (with detailed solutions)Subject: Mathematics Age range: 11-14 Resource type: Worksheet/Activity  Last updated 2 October 2020
Creative Commons "Sharealike" Your rating is required to reflect your happiness. It's good to leave some feedback. Something went wrong, please try again later. sarimarta59thank you for your worksheet Empty reply does not make any sense for the end user Thank you for sharing.<br /> Thank you so much for generously sharing your resources - it is appreciated! Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch. Not quite what you were looking for? Search by keyword to find the right resource:WORD PROBLEMS ON AREA AND CIRCUMFERENCE OF A CIRCLEProblem 1 : A cylindrical tank has radius 1.5 m. What is the circumference of its base ? A cylindrical tank has the base which is in the shape of circle. Circumference of base = 2πr radius (r) = 1.5 m Circumference of the base = 2(3.14)(1.5) = 9.42 m 2 So, circumference of the base is 9.42 m 2 . Problem 2 : A circular pond has diameter 8 m and needs to be fenced for the protection of children. a) What length of fencing is required? b) Fencing comes in 1 m lengths. How many lengths are needed? c) What is the total cost of the fencing if each length costs $25.00? Diameter of the circular pond = 8 m, radius = 4 m (a) Length of fencing = Circumference of circle = 2 πr = 2(3.14) (4) = 25.12 So, length of fencing is 25.12 m. (b) Length of each fencing = 1 m Number of fencing required = 26 (c) Cost of each fencing = $25 Required cost = 25 (26) = $650 So, the required cost is $650. Problem 3 : A car wheel has a radius of 35 cm. a) What is the circumference of the wheel? b) If the wheel rotates 100 000 times, how far does the car travel? Radius of wheel = 35 cm Circumference of the wheel = 2 πr = 2(3.14) (35) = 219.8 So, circumference of the circle is 220 cm. (b) Distance covered in 100 000 times = 100000(220) = 22000000 cm 100 cm = 1 m and 1000 m = 1 km = 22000000/100000 = 220 km So, distance covered by the car is 220 km. Problem 4 : A trundle wheel is used for measuring distances. The circumference of the wheel is exactly 1 m. Each time the wheel rotates through one complete turn a click sound is heard and a counter adds a meter to the total. What is the radius of this wheel?  Circumference of circle = 1 m 2 πr = 1 2(3.14) r = 1 6.28r = 1 r = 1/6.28 r = 0.159 m 100 cm = 1 m and 1 cm = 10 mm r = 159 mm So, the required radius is 159 mm. Problem 5 : A circular garden plot has circumference 12.65 m. Find its radius in meters, correct to the nearest centimetre. Circumference of circular garden = 12.65 m 2 πr = 12.65 2(3.14)r = 12.65 r = 12.65/6.28 r = 2.01 m So, radius of the circular garden is 2.01 m. Problem 6 : An irrigation sprinkler sprays water over a field. The radius of the spray is 12.6 m. What area of the field is being watered? Radius of the spray = 12.6 m Area of the field is being watered = Area of circle = πr 2 = 3.14(12.6) 2 = 3.14(158.76) = 498.50 So, area of the field is being watered is 498.50 m 2 Problem 7 : The rope connecting a goat to a pole is 8 m long. What area of grass can the goat eat? Length of rope = 8 m Area of grass can the goat eat = πr 2 = 3.14(8) 2 = 200.96 = 201 m 2 So, area of grass can the goat eat is 201 m 2 . Problem 8 : A circular hoop has a radius of 40 cm. Find the length of tubing needed to make the hoop. Radius of circular hoop = 40 cm Length of tubing needed to make a hoop = 2 πr = 2(3.14)(40) = 251.2 So, length of tubing needed is 251.2 cm. Problem 9 : 6 identical metal discs are stamped out of an 18 cm by 12 cm sheet of copper as illustrated. What percentage of the copper is wasted  Area of 6 stamps = 6 πr 2 3(diameter of circle) = 18 3(2r) = 18 r = 18/6 r = 3 cm Area = 6(3.14)(9) Area of metal discs cut out = 169.56 cm 2 Copper wasted = Area of rectangular sheet - Area of metal discs cut out = 18 x 12 - 169.56 = 216-56.52 = 46.44 = (46.44/216) ⋅ 100% = 21.5% So, copper wasted is 21.5%. Problem 10 : A table-top is shaped as illustrated. A cloth to protect the table-top from stains and heat is cut exactly the same size as the table-top. It is made from fabric 1.6 m wide and costs $18.40 per metre of length. a) What length of fabric must be purchased? b) Calculate the cost of the fabric. c) Find the area of the cloth. d) Calculate the amount of fabric that is wasted.  (a) Length of fabric to be purchased = Side length of one side = 2.4 + 0.8 + 0.8 = 4 m So, length of fabric to be purchased is 4 m. (b) Cost of fabric = $18.40 Cost of fabric purchased = 18.40(4) = $73.60 (c) Area of cloth = Area of rectangle in the middle + 2(Area of semicircle) = 2.4(1.6) + 2( πr 2 /2) = 3.84 + (3.14)(0.8) 2 = 3.84 + 2.0096 = 5.85 m 2 d) Amount of fabric wasted = (2.4+16) x 1.6 - 2.0096 = 6.4 - 5.85 = 0.55 m 2  Apart from the stuff given above, i f you need any other stuff in math, please use our google custom search here. Kindly mail your feedback to [email protected] We always appreciate your feedback. © All rights reserved. onlinemath4all.com
Recent ArticlesBest way to learn mathematics. Jun 25, 24 04:56 PM Problems on Solving Logarithmic EquationsJun 24, 24 05:48 PM SAT Math Preparation Videos (Part - 2)Jun 24, 24 01:38 AM MathBootCampsArea of a circle – formula and examples. The area of a circle can be thought of as the number of square units of space the circle occupies. This can be found using either the radius or the diameter, which we will cover in the examples below. We will also look at some examples of word problems involving area that you may come across in your studies. [adsenseWide] Examples of finding the area of a circleWe will use the following formula to find the area of any circle. Notice that this formula uses the radius, so we will have to convert when we are given the diameter instead. Let’s look at both cases.  Example (given radius)Find the area of a circle with a radius of 5 meters. Apply the formula: \(A = \pi r^2\) with radius \(r = 5\). Remember that \(\pi\) is about 3.14. \(\begin{align}A &= \pi (5)^2 \\ &= 25\pi \\ &\approx \bbox[border: 1px solid black; padding: 2px]{75.5 \text{ m}^2}\end{align}\) A few comments about this final answer. Since the units of the radius were in meters, the answer is in square meters. This can be written out in words, or as \(\text{m}^2\). Also, the final answer can be written in terms of \(\pi\) (\(25 \pi\) square meters) or as a decimal approximation (75.5 square meters). Which one you use depends on the application and the problem you are working on. Example (given diameter)Find the area of a circle with a diameter of 6 feet. The radius of any circle is always half the diameter. Since the diameter of the circle is 6 feet, the radius must be 3 feet (the radius is always half of the diameter). So, we can apply the formula using \(r = 3\). \(\begin{align}A &= \pi (3)^2 \\ &= 9\pi \\ &\approx \bbox[border: 1px solid black; padding: 2px]{28.3 \text{ ft}^2}\end{align}\) As you can see, it is important to pay attention to whether or not you are given the radius or the diameter of the circle. In some word problems though, this may not always be as clear. Word problems involving the area of a circleNot every problem you will encounter will simply say “find the area”. In the next two examples, you will see other types of questions you might be asked. Jason is painting a large circle on one wall of his new apartment. The largest distance across the circle will be 8 feet. Approximately how many square feet of wall will the circle cover? Whenever you are asked to find the number of square feet covered by something, you are finding an area. To find the area of Jason’s circle, we first need to figure out if we have been given the radius or the diameter. By definition, the diameter of a circle is the longest distance across the circle, so we know here that the diameter is 8 feet. This means that the radius is 4 feet. Therefore: \(\begin{align}A &= \pi (4)^2 \\ &= 16\pi \\ &\approx \bbox[border: 1px solid black; padding: 2px]{50.2 \text{ square feet}}\end{align}\) So, Jason’s circle will cover about 50.2 square feet of his wall. The area of a circle is \(81 \pi\) square units. What is the radius of this circle? To answer this question, you will have to remember a little bit of algebra. Use the formula and substitute the values you know. Then, solve for the radius, \(r\). Start with the area formula. \(A = \pi r^2\) Substitute in \(A = 81 \pi\) since you know this is the area. \(81\pi = \pi r^2\) Divide both sides by \(\pi\). \(81 = r^2\) This can also be written as: \(r^2 = 81\) Take the square root to find \(r\). Since this is a radius, the value of \(r\) must be positive. \(\begin{align}r &= \sqrt{81} \\ &= \bbox[border: 1px solid black; padding: 2px]{9}\end{align}\) Therefore, the radius must be 9. [adsenseLargeRectangle] Finding the area of a circle is all about applying the formula. But be careful! You always must pay attention to the information you are given – especially in applied problems. Share this:
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Find support for a specific problem in the support section of our website. Please let us know what you think of our products and services. Visit our dedicated information section to learn more about MDPI. JSmol ViewerExploring the nature of diversity dishonesty within predominantly white schools of medicine, pharmacy, and public health at the most highly selective and highly ranked u.s. universities.  Share and CiteBurrell, D.N. Exploring the Nature of Diversity Dishonesty within Predominantly White Schools of Medicine, Pharmacy, and Public Health at the Most Highly Selective and Highly Ranked U.S. Universities. Soc. Sci. 2024 , 13 , 332. https://doi.org/10.3390/socsci13070332 Burrell DN. Exploring the Nature of Diversity Dishonesty within Predominantly White Schools of Medicine, Pharmacy, and Public Health at the Most Highly Selective and Highly Ranked U.S. Universities. Social Sciences . 2024; 13(7):332. https://doi.org/10.3390/socsci13070332 Burrell, Darrell Norman. 2024. "Exploring the Nature of Diversity Dishonesty within Predominantly White Schools of Medicine, Pharmacy, and Public Health at the Most Highly Selective and Highly Ranked U.S. Universities" Social Sciences 13, no. 7: 332. https://doi.org/10.3390/socsci13070332 Article MetricsFurther information, mdpi initiatives, follow mdpi.  Subscribe to receive issue release notifications and newsletters from MDPI journals |
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Area of a Circle Practice Problems with Answers. There are twelve (12) practice problems in this exercise about the area of the circle. You may use a calculator. Do not round intermediate calculations. Round your final answer to two decimal places unless the exact answer is required.
The Corbettmaths Practice Questions on the Area of a Circle. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths ... Click here for Questions. Click here for Answers. circles. Practice Questions. Previous: Arc Length Practice Questions. Next: Area of a Sector Practice Questions. GCSE ...
The other way to solve this problem is to divide the diameter by 2 to get the radius and follow the regular area of the circle formula with radius. Question 2: Find the area of the circle whose radius is 32 units. Solution: Given the radius is 32 units. Area of circle = πr2. = 22/7 × 32 × 32. = (22 × 32 × 32 ) / 7.
Find the area of a circle with a circumference of 12.56 units. units 2. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
Example 1 : calculating the area of the circle given the radius. A circle has a radius of 6\mathrm {~cm}. 6 cm. Calculate its area. Give your answer to 2 \text { dp}. 2 dp. Find the radius of the circle. The length of the radius is given in the question, r=6\mathrm {~cm}. r = 6 cm.
Calculate the area of the shaded region. Give your answer to 2 decimal places. 6. A circular flower bed has diameter 7 metres. Work out the area of the flower bed. Give your answer correct to 1 decimal place. 7. Shown below is a circular photo surrounded by a frame. The photo has radius 12cm.
So, the area of a circle with a diameter of 63 cm is 3118.5 square cm. Remember, you can also find the radius by dividing the diameter by 2 and use the formula πr 2 to solve this problem. Question 2: What is the area of a circle with a radius of 32 units? Solution:
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ... Area and circumference challenge problems. Finding circumference of a circle when given the area. ... Finding circumference of a circle when given the area . Video 1 minute 31 seconds 1:31. Area of a shaded ...
Practice Finding the Area of a Circle with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost your Algebra grade with Finding the Area of a ...
To find the area of a circle, we need to find the radius first. The radius of the circle is half of the diamter which is half of 7 = 3.5 inches. Next we need to square the radius: 3.5 2 = 3.5 x 3.5 = 12.25 cm. Finally we need to multiply this amount by pi (π). So the area of this circle is π x r 2 = π x 12.25 cm.
Find the area the circle with a diameter of 10 inches. Solution: Step 1: Write down the formula: A = πr 2. Step 2: Change diameter to radius: Step 3: Plug in the value: A = π5 2 = 25π. Answer: The area of the circle is 25π ≈ 78.55 square inches. Example 2:
A circle has a radius of 6cm 6cm, calculate its area. Give your answer to 2dp 2dp. Find the radius of the circle. The radius is given in the question. Radius =6cm = 6cm. 2 Use the formula \pi r^2 πr2 to calculate the area of the circle. \begin {aligned} &\pi r^2\\\\ &= \pi \times r\times r\\\\ &= \pi \times6\times 6\\\\ &= 36\pi \\\\ &= 113. ...
Since we have that the diameter is 3 m, we divide it by 2 to get the radius which then is 1.5 m. Plugging values into the equation, we have: A = π (3 / 2 m)) 2. A = π (2.25 m 2) A = 2.25π m 2. Complexity=4, Mode=fraction. Find the area. Use 22/7 as an approximation for π, but give the final answer in decimal.
Area, circumference, diameter and radius. Area and circumference both relate to the radius and diameter of a circle. Once you know one, you can find all of the others -- It just takes a little math!
Solved Problems on Circle. Let us understand the concepts related to circles along with the following questions-. Example 1: To cover a distance of 10 km, a wheel rotates 5000 times. Find the radius of the wheel. Solution: Number of rotations = 5000. Total distance covered = 10 km. Let 'r' be the radius of the wheel.
MATH MONKS 1 Word Problems Area and Circumference of a Circle - Answers Sohan purchased a wall clock. The radius of the clock is 20 cm. What is the area and circumference of the wall clock ? Area = 1256.63 cm2, Circumference = 125.66 cm Pamela bought a new Fiat- four wheeler car. The radius of the wheel is 36 in. Find the
Click here for Questions. Circles. Textbook Exercise. Previous: Area of Compound Shapes Textbook Exercise. Next: Types of Angles Textbook Exercise. The Corbettmaths Textbook Exercise on the Area of Circles.
Circle Worksheets. This generator makes worksheets for calculating the radius, diameter, circumference, or area of a circle, when one of those is given (either radius, diameter, circumference, or area is given). They can be made in PDF or html formats. Options are numerous: you can choose metric or customary units or both, you can include or ...
The area of a circle is size of the surface of the circle. The formula is πr 2. The area of the circle is expressed in square units. Since the formula is only given in terms of radius, remember to change from diameter to radius when necessary. Read the lesson on area of circle if you need to learn how to calculate the area of a circle.
Area of a Circle (with detailed solutions) Two worksheets focusing on finding areas of circles and circular shapes. Problem-type questions are included as well. I find that these sheets are very useful as homework tasks for Y8 and older. As an extra, I have included a NEW STYLE of PowerPoint, which allows questions and solutions to be easily ...
Area of the field is being watered = Area of circle = πr 2 = 3.14(12.6) 2 = 3.14(158.76) = 498.50. So, area of the field is being watered is 498.50 m 2. Problem 7 : The rope connecting a goat to a pole is 8 m long. What area of grass can the goat eat? Solution : Length of rope = 8 m. Area of grass can the goat eat = πr 2 = 3.14(8) 2
Word problems involving the area of a circle. Not every problem you will encounter will simply say "find the area". In the next two examples, you will see other types of questions you might be asked. Example. Jason is painting a large circle on one wall of his new apartment. The largest distance across the circle will be 8 feet.
A semicircle having centre at O and radius equal to 4 is drawn with PQ as the diameter as shown is the figure given below. OSRU is a rectangle such that the ratio of area of the semicircle to the area of the rectangle is 2π: 3 or cuts the semicircle at T. Find the length of line segment TQ. A. (8/5)√5. B. (5/3)√5. C. (17/9)√5. D. (9/2)√5.
Recognizing the critical need to address diversity dishonesty, this article comprehensively explores frameworks to understand and combat this phenomenon. It seeks to engage with viable theories, problem-solving approaches, and contextual models that can illuminate the complex interplay of factors contributing to diversity dishonesty.