7th Grade Circumference and Area of Circles Test with Point Values (PDF)

7th Grade math test: Circumference and Area of Circles – Maths PDF

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This circles test for 7th Grade covers circumference and area of circles (Common Core 7.G.B.4), with a free PDF to print.

This 45-minute test checks the circumference and area of circles, the meaning of pi, radius and diameter, and semicircles and composite figures (Common Core 7.G.B.4). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Circumference and Area of Circles
Standards: 7.G.B.4
Time: 45 minutes
Total: 20 points

Circles test: questions

Question 1 – Circumference [2 pts]

A circle.

Find the circumference of the circle. Use \(\pi\approx\frac{22}{7}\).

Question 2 – Area [2 pts]

A circle.

Find the area of the circle. Use \(\pi\approx 3.14\).

Question 3 – Find the radius [2 pts]

A circle has a circumference of 62.8 ft. Find the radius and then the area. Use \(\pi\approx 3.14\).

Question 4 – Leave it in pi [2 pts]

A circle has a radius of 12 m. Write the circumference and the area in terms of \(\pi\).

Question 5 – Semicircle [2 pts]

A semicircle.

Find the perimeter and the area of the semicircle. Use \(\pi\approx 3.14\).

Question 6 – Wheel distance [2 pts]

A wheel has a radius of 15 in. How many inches does it roll in 5 turns? Use \(\pi\approx 3.14\).

Question 7 – Leftover metal [2 pts]

A circle cut from a square.

A circle of radius 10 in is cut from a 20-in square. Find the area of the leftover metal. Use \(\pi\approx 3.14\).

Question 8 – Track [3 pts]

A track made from a rectangle and two semicircles.

Find the distance around the track (two straight sides of 40 m and two semicircles of diameter 20 m). Use \(\pi\approx 3.14\). (1 point)
Find the area enclosed. (1 point)
A runner completes 5 laps. Find the distance run. (1 point)

Question 9 – Rug with a hole [3 pts]

A circular rug with a hole.

Find the area of the outer circle. (1 point)
Find the area of the inner circle. (1 point)
Find the area of the rug itself (the ring). Use \(\pi\approx 3.14\). (1 point)

Key facts behind this circles test

Key facts

Diameter \(d = 2r\); radius is half the diameter.
Circumference \(C = \pi d = 2\pi r\).
Area \(A = \pi r^2\) (square the radius first).
\(\pi\) is about \(3.14\) or \(\frac{22}{7}\); leave answers in terms of pi to be exact.
A semicircle has half the area of the circle; its perimeter adds the diameter.

How to use this circles test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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