circle problem solving worksheet

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

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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. units (mm, cm, m, km, mm , cm , m , km ) units (in, ft, yd, mi, in , ft , yd , mi ) Bordercolor: Font Size:  Additional title & instructions  (HTML allowed) Key to Geometry Workbooks Here 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. 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Catering to the learning needs of students in grade 5 through grade 8, these printable worksheets practice the topic pretty much across the board: easy, moderate and hard. The job in the easy set is to calculate the area and circumference of the circles with radius ranging from 1 to 25. The moderate set requires rounding answers to tenth place with the radius of circles ranging between 25 and 100. In the hard worksheets, the radius is rendered in decimal and the task is to round your answers to two decimal places. Use pi = 3.14 wherever necessary. Explore some of these worksheets for free! Area from Radius Applying the formula, Area = pi * r 2 , find the area of each circle. Download the set Area from Diameter Find the radius from diameter and apply the formula to find the area of a circle. Area from Radius or Diameter Each printable worksheet has 9 problems on finding area of a circle with the known radius or diameter. Two simple word problems and one story problem included. Area and Circumference: Combined Review These are the perfect review worksheets in finding both area and circumference of the circle. Radius or Diameter from Area Dividing the area by pi or 3.14, you get r 2 . Taking the square root, you get radius. Solve each problem based on this technique. Area from Circumference Find the area from the circumference of each circle in this stock of worksheets for 7th grade students. Word problems included to understand real-life application. Circumference from Radius Applying the formula, Circumference = 2 * pi * r, find the circumference of each circle. Circumference from Diameter To find the circumference, multiply diameter with pi value. Each pdf worksheet has 9 problems. Circumference from Radius or Diameter Circumference of a circle worksheet contains six standard problems and two word problems. Radius or Diameter from Circumference Divide the circumference by pi or 3.14. You get the diameter. Answer the questions. Circumference from Area Each worksheet has 8 problems finding circumference from area of a circle. Simple word problems included. Area of an Annulus Worksheets Imagine two circles with different radii, but the same center; can you calculate the area of the region in between? Scout around these pdf worksheets, pore over the examples, and solve similar problems on area of an annulus! (9 Worksheets) Related Worksheets » Arc Length and Area of Sector » Area of Segment » Area of Compound Shapes » Area of Mixed Shapes Become a Member Membership Information Printing Help How to Use Online Worksheets How to Use Printable Worksheets Privacy Policy Terms of Use Copyright © 2024 - Math Worksheets 4 Kids This is a members-only feature! 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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

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Area of a Circle Worksheets

Area of a circle word problems.

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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

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Circles: Radius, Diameter, Circumference, Area

Print out these worksheets on circles.  Practice naming circles and calculating circumference, radius, diameter, and area of a circle.

Circumference and Area (Intermediate)

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Circle Word Problems Worksheets

Related Topics: More Math Worksheets More Printable Math Worksheets More Grade 7 Math Lessons

Printable “Circle” worksheets: Circumference Worksheets Area of Circle Worksheets Area & Circumference Worksheets Find Radius from Circumference Find Radius from Area Find Area from Circumference or vice versa Circle Word Problems

Examples, solutions, videos, and worksheets to help Grade 7 students review how to solve word problems involving circles.

How to solve word problems involving circles?

Solving Problems of Shapes Involving Circles To solve problems involving shapes that include circles or parts of circles, follow these steps:

• Understand the Problem: Read the problem carefully and identify the type of shapes involved (full circles, semi-circles, quarter-circles, sectors, composite shapes).
• Identify Given Information: Note any provided measurements such as radii, diameters, angles, and dimensions of other shapes.
• Apply Relevant Formulas: Use appropriate formulas for areas and circumferences of circles and related shapes.
• Perform Calculations: Execute the necessary mathematical operations to find the required areas.
• Combine Results: For composite shapes, sum or subtract the areas of individual components as required.
• Verify Your Solution: Ensure the solution makes sense in the context of the problem.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Circle Word Problems Worksheets .

More Circle Word Problems Worksheets

Printable (Answers on the second page.) Circle Word Problems Worksheet #1 Circle Word Problems Worksheet #2 Circle Word Problems Worksheet #3 Circle Word Problems Worksheet #4 Circle Word Problems Worksheet #5

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Circumference and Area of Circles (A)

Welcome to The Circumference and Area of Circles (A) Math Worksheet from the Measurement Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2010-03-06 and has been viewed 196 times this week and 196 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Circle worksheets: finding the area

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Worksheet on Circle

In worksheet on circle we will solve different types of question in circle.

1.  The following figure shows a circle with centre O and some line segments drawn in it. Classify the line segments as radius, chord and diameter:

(i) OA = ………………..

(ii) OB = ………………..

(iii) OC = ……………….. (iv) EF = ……………….. (v) MN = ……………….. (vi) PQ = ………………..

2. Observe the circles given below and identify.

(a) OT, OS, OP, OR

3. Observe the circles given below and identify.

4. Draw a radius, diameter, chord in the given circle using the points. Also measure the length of radius and diameter.

(i) OB, OA, OC = 2 cm

(ii) BC = 4 cm

(iii) 

5. With the help of a compass, draw a circle of radius:

(i) 4.5 cm. (ii) 5.2 cm

6. Draw a circle of radius 6 cm.

7. Draw a circle of diameter 5.5 cm.

8. Draw a circle with centre C and radius 4.7 cm. Mark point P,Q,R such that P lies in the interior of the circle, Q lies on the circle and R lies in the exterior of the circle.

9. Draw a circle using ruler and compass.

(i) Radius = 4 cm

(ii) Diameter = 6 cm

(iii) Diameter = 8 cm

(iv) Radius = 3.5 cm

10. Draw a circle whose diameter is 10 cm. Find its radius.

11. Find the radius if the diameter of the circle is:

12. Find the diameter if the radius of the circle is:

(iii) 10 cm

(iii) 20 cm

13. With a same circle, draw three circles first with radius 2 cm. second with radius 3 cm and third with radius 4 cm.

14. A circle has a radius 7 cm. Find the length of the longest chord of this circle.

15. State whether each of the following statement is true or false.

(i) Each radius of a circle is also a chord of the circle ............ .

(ii) Each diameter of a circle is also a chord of the circle ............ .

(iii) The centre of a circle bisects each chord of the circle ............ .

(iv) A circle is a polygon

(v) A circle is a closed figure without corners.

(vi) The chord of a circle is also its radius.

(vii) The chord of a circle can be equal to the diameter of a circle.

(viii) The diameter represents the length of a circle.

(i) False 

(iii) False

(viii) False

16. Multiple Choice Questions (MCQ) on Circle:

    Tick ( ✔ )  the correct option.

(i) In a circle, the area bounded by an arc and two radii joining the centre to the end- points of the arc is called a

(a) sector;     (b) segment;     (c) arc;     (d) secant

(ii) The radius of a circle of diameter 20.4 cm is

(a) 20.4 cm;     (b) 11.8 cm;     (c) 10.2 cm;     (d) 5.1 cm

(iii) The area bounded by a diameter and the semicircle is called

(a) minor segment;     (b) major segment;     (c) semi-circular region;     (d) perimeter

16.  (i) (a) sector

(ii) (c) 10.2 cm

(iii) (c) semi-circular region

17. From the adjoining figure, name the following:

17.  (i) OA, AO

(iv) BC, BPQAC

18. A circle with centre I is given below. Fill in the blanks:

(i) IM is the __________ of the circle.

(ii) HQ is the __________ of the circle.

(iii) PQ is the __________ of the circle.

(iv) PM is an __________ of the circle.

(v) The name of the circumference of the circle is __________.

18.  (i) radius

(iii) radius

19. Find the radius of the circle whose diameter is:

(iii) 30 cm

(vii) 36 cm (viii) 44 cm

19.  (i) 10 cm

(iii) 15 cm

(vii) 18 cm (viii) 22 cm

20. Find the diameter of the circle whose radius is:

(iii) 12 cm

20.  (i) 8 cm

(iii) 24 cm

21. Fill in the blanks:

(i) A circle consists of an infinite number of __________. 

(ii) All radii of a circle are __________. 

(iii) The longest chord of a circle is known as __________. 

(iv) The boundary of a circle is known as its __________. 

21.  (i) raddi

(ii) equal.

(iii) diameter

circumference

22. If the diameter of a pan pizza is 18 cm, then find the length of the straight sides of the pizza slice.

(i) Diameter = ………………

(ii) Radius = ………………

(iii) Side of the pizza slice.

23. Fill in the blanks:

(i) A diameter of a circle is a chord that ………..through the centre.

(ii) A radius of a circle is a line segment with one end point ………….. and the other end…………… .

(iii) If we join any two points on a circle by a line segment. We obtain a …………… of the circle.

(iv) Any part of a circle is called an ……………. of the circle.

24. Choose the right answer. 

(i) The circle with a radius 6 cm will have the diameter of __________.

(a) 11 cm          (b) 12 cm          (c) 13 cm          (d) 14 cm

(ii) A circle has __________ lines of symmetry.

(a) 5          (b) 10          (c) 15          (d) infinite

24.  (i) (b) 12 cm

(ii) (d) infinite

25. For the given circle:

26. Using a compass draw a circle of radius 5 cm. Name its centre as P. Draw and mark:

(i) A radius LN

(ii) A diameter XY.

To download the above Worksheet on Circle  Click Here.

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●   Circle

Relation between Diameter Radius and Circumference.

Worksheet on Circle.

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