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 ฯ€\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 (ฯ€r\pi r). So the area is rร—ฯ€r=ฯ€r2r \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 ฯ€\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 ฯ€\pi.

Example 4

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

Example 7

challenge
A circle is inscribed in an equilateral triangle of side 66. (Skip exact โ€” 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 ฯ€\pi.

Example 9

easy
Find the area of a circle with radius 55. (In terms of ฯ€\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 ฯ€โ‰ˆ3.14\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 ฯ€\pi.

Example 14

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

Example 15

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

Example 16

medium
A pizza has radius 88 inches. What is its area? (Use ฯ€โ‰ˆ3.14\pi \approx 3.14.)

Example 17

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

Example 18

medium
A circular pool has area 144ฯ€144\pi mยฒ. 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 ฯ€\pi.)
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