Circles: circumference and area worksheet

Grade 7 math, Common Core 7.G.B.4. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Circles: circumference and area

Grade 7 math, Common Core 7.G.B.4

Use 3.14 for π. Round to the nearest hundredth.

1.
Find the area of a circle with a diameter of 8 m. Leave your answer in terms of π.
2.
Find the area of a circle with a diameter of 26 ft. Leave your answer in terms of π.
3.
Find the area of a circle with a radius of 14 m.
4.
A circle has a circumference of 25.12 ft. What is its diameter?
5.
Find the circumference of a circle with a radius of 2 cm.
6.
Find the circumference of a circle with a radius of 7 in.
7.
Find the circumference of a circle with a diameter of 28 m.
8.
Find the circumference of a circle with a radius of 11 in.
9.
Find the area of a circle with a radius of 7 ft.
10.
Find the area of a circle with a diameter of 28 m. Leave your answer in terms of π.

Answer key: Circles: circumference and area

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 16π m²
r = 4A = π × 4² = 16π
2. 169π ft²
r = 13A = π × 13² = 169π
3. 615.44 m²
A = 3.14 × 14² = 3.14 × 196 = 615.44
4. 8 ft
d = C ÷ 3.14 = 25.12 ÷ 3.14 = 8
5. 12.56 cm
C = 2 × 3.14 × 2 = 12.56
6. 43.96 in
C = 2 × 3.14 × 7 = 43.96
7. 87.92 m
C = 3.14 × 28 = 87.92
8. 69.08 in
C = 2 × 3.14 × 11 = 69.08
9. 153.86 ft²
A = 3.14 × 7² = 3.14 × 49 = 153.86
10. 196π m²
r = 14A = π × 14² = 196π

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About circles: circumference and area

The circumference is the distance around a circle: C = πd, or C = 2πr. The area is the space inside: A = πr². The radius r is half the diameter d. π is about 3.14, so a circle’s circumference is a bit more than 3 times its diameter.

Worked example 1

Find the circumference of a circle with a diameter of 22 ft.

Step 1.C = 3.14 × 22 = 69.08

Answer: 69.08 ft

Worked example 2

A circle has a circumference of 25.12 in. What is its diameter?

Step 1.d = C ÷ 3.14 = 25.12 ÷ 3.14 = 8

Answer: 8 in

Worked example 3

Find the area of a circle with a radius of 10 m.

Step 1.A = 3.14 × 10² = 3.14 × 100 = 314

Answer: 314 m²

Watch out for

Check whether you were given the radius or the diameter. The radius is half the diameter.
In A = πr², square the radius before multiplying by π.
Circumference is a length (cm); area is in square units (cm²).

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