Practice Area of a Circle in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The amount of space enclosed inside a circle, calculated as π\pi times the square of the radius.

Imagine cutting a pizza into many thin slices and rearranging them into a shape that looks like a rectangle. The 'height' of that rectangle is the radius rr, and the 'width' is half the circumference (πr\pi r). So the area is r×πr=πr2r \times \pi r = \pi r^2.

Showing a random 20 of 50 problems.

Example 1

easy
Find the area of a circle with radius 66 cm. Leave your answer in terms of π\pi.

Example 2

challenge
A circle of radius rr has the same area as a square of side ss. Express ss in terms of rr.

Example 3

medium
A circle is inscribed in a square whose perimeter is 4040. Find the area of the circle in terms of π\pi.

Example 4

easy
A circle has diameter 1414 cm. Find its area in terms of π\pi.

Example 5

easy
If a circle's radius doubles, what happens to its area?

Example 6

medium
A square has a circle inscribed in it. The square has side 1010. Find the circle's area. (In terms of π\pi.)

Example 7

challenge
A circle is inscribed in an equilateral triangle of side 66. (Skip exact — set up.) What's the radius of the inscribed circle?

Example 8

hard
A circle is inscribed in a square of side 1212. Find the area inside the square but outside the circle, in terms of π\pi.

Example 9

easy
Find the area of a circle with radius 55. (In terms of π\pi.)

Example 10

medium
If a circle's radius is tripled, by what factor does its area grow?

Example 11

medium
A circular tabletop has radius 0.60.6 m. Find its area to two decimal places, using π≈3.14\pi \approx 3.14.

Example 12

challenge
A circle has the same area as an equilateral triangle of side 66. Find the circle's radius exactly.

Example 13

medium
A semicircle has diameter 1212. Find its exact area in terms of π\pi.

Example 14

easy
A circle has diameter 1010. Find its area in terms of π\pi.

Example 15

medium
Find the area of an annulus with outer radius 1010 and inner radius 66, in terms of π\pi.

Example 16

medium
A pizza has radius 88 inches. What is its area? (Use π≈3.14\pi \approx 3.14.)

Example 17

easy
Find the circumference of a circle with radius 77. (In terms of π\pi.)

Example 18

medium
A circular pool has area 144π144\pi m². What is its diameter?

Example 19

easy
True or false: doubling the diameter quadruples the area of a circle.

Example 20

medium
Find the area between two concentric circles (an annulus) with radii 33 and 55. (In terms of π\pi.)
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