Practice Pi (π) in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The ratio of a circle's circumference to its diameter, approximately 3.14159…3.14159\ldots

No matter how big or small the circle, circumference ÷\div diameter always equals π\pi.

Showing a random 20 of 50 problems.

Example 1

medium
A circle has a radius of 7 m. Find its area. Use π≈3.14\pi \approx 3.14.

Example 2

easy
A circle's circumference is C=62.8C = 62.8 cm. What is its diameter? Use π≈3.14\pi \approx 3.14.

Example 3

medium
A circular garden has area 50.2450.24 m2^2. Find its radius using π≈3.14\pi \approx 3.14.

Example 4

challenge
A circle is inscribed in an equilateral triangle of side 66 cm. Find the area of the circle in terms of π\pi.

Example 5

easy
A circle has radius 66 cm. Find its area in terms of π\pi.

Example 6

challenge
Ancient mathematicians estimated π\pi by inscribing regular polygons in a circle. Explain why a regular polygon's perimeter, divided by the circle's diameter, approaches π\pi as the number of sides increases.

Example 7

medium
A square and a circle have the same perimeter/circumference of 4π4\pi. Which has the larger area?

Example 8

hard
A pendulum of length 22 m swings through an arc whose central angle is 30∘30^\circ. Find the arc length in terms of π\pi.

Example 9

hard
A circle is inscribed in a square of side 1010 cm. Find the area of the region inside the square but outside the circle, in terms of π\pi.

Example 10

easy
What is π\pi in degrees of arc? (i.e., π\pi radians = ? degrees)

Example 11

hard
A wheel of radius 0.5 m rolls without slipping. How many full rotations does it make to travel 100 m? Use π≈3.14159\pi \approx 3.14159.

Example 12

medium
A circle has area 36π36\pi cm2^2. Find its circumference in terms of π\pi.

Example 13

easy
True or false: the ratio C/dC/d is larger for a bigger circle.

Example 14

challenge
Two pulleys of radius 33 are connected by a tight belt, their centers 1010 apart. Find the total length of the belt in terms of π\pi.

Example 15

hard
A running track is a rectangle 8080 m by 5050 m with semicircles capping the short ends. Find the total distance around the track in terms of π\pi.

Example 16

easy
A circle has diameter 77. Find its circumference in terms of π\pi.

Example 17

easy
If a circle's diameter doubles, by what factor does its circumference grow?

Example 18

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

Example 19

hard
Two circles have radii 33 and 44. A third circle has area equal to the sum of their areas. Find its radius.

Example 20

medium
A circular track has radius 5050 m. A runner completes 4 laps. About how far did they run? Use π≈3.14\pi \approx 3.14.
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