Practice Circumference 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 total distance around the outside of a circle; equal to Ο€\pi times the diameter or 2Ο€r2\pi r.

Imagine wrapping a string tightly around a circular jar lid, then straightening the string out. That length is the circumference. No matter the size of the circle, the circumference is always Ο€\pi times the diameterβ€”roughly 3.143.14 laps of the diameter around the edge.

Showing a random 20 of 50 problems.

Example 1

medium
A clock's minute hand is 77 cm long. How far does its tip travel in one hour? Use Ο€β‰ˆ22/7\pi\approx 22/7.

Example 2

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The perimeter of a semicircular region (arc plus diameter) of radius 10 is what, in terms of Ο€\pi?

Example 3

hard
A circular running track has circumference 400400 m. A runner completes 55 laps. Find the distance.

Example 4

medium
A wire of length 6666 cm is bent into a circle. Find its radius using Ο€β‰ˆ22/7\pi\approx 22/7.

Example 5

medium
Two circles have radii in ratio 2:5. What is the ratio of their circumferences?

Example 6

hard
A circle is inscribed in a square of side 1414. Find the difference between the square's perimeter and the circle's circumference. Use Ο€β‰ˆ22/7\pi\approx 22/7.

Example 7

easy
A circle has circumference 30Ο€30\pi. Find its radius.

Example 8

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If a circle's radius is tripled, what happens to the circumference?

Example 9

challenge
A wheel rolls one full revolution without slipping. The center moves how far in terms of the radius rr?

Example 10

challenge
A circular sector has arc length 8Ο€8\pi and central angle 240∘240^\circ. Find the radius.

Example 11

medium
Find the arc length of a 120∘120^\circ sector in a circle of radius 99 in terms of Ο€\pi.

Example 12

hard
Find the arc length corresponding to a central angle of 11 radian in a circle of radius 55.

Example 13

easy
A bicycle wheel has radius 0.35 m. How far does it travel in one full rotation? (Use Ο€β‰ˆ3.14\pi \approx 3.14.)

Example 14

hard
Two pulleys of radius 55 are 2020 apart. Find the belt length using Ο€β‰ˆ3.14\pi\approx 3.14.

Example 15

easy
A circle has diameter 14. Find its circumference using Ο€β‰ˆ22/7\pi \approx 22/7.

Example 16

hard
A regular hexagon has perimeter 4848. Find the circumference of its circumscribed circle in terms of Ο€\pi.

Example 17

easy
If you double a circle's radius, what happens to its circumference?

Example 18

easy
A circle has radius 77. Find its circumference in terms of Ο€\pi.

Example 19

easy
What ratio does Ο€\pi represent?

Example 20

easy
Find the circumference of a circle with diameter 1414 cm. Leave your answer in terms of Ο€\pi.
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