Success Homeschool

Year 8 Mathematics · Circles: circumference and area

Name: ______________________

Date: ____________

1. A circle has a radius of 4 cm. What is its diameter?
- ☐ (a) 2 cm
- ☐ (b) 8 cm
- ☐ (c) 16 cm
- ☐ (d) 12.56 cm
2. Which formula gives the area of a circle?
- ☐ (a) A = πd
- ☐ (b) A = 2πr
- ☐ (c) A = πr^2
- ☐ (d) A = 2r
3. Find the circumference of a circle with diameter 20 cm, using π ≈ 3.14.
- ☐ (a) 125.6 cm
- ☐ (b) 31.4 cm
- ☐ (c) 314 cm
- ☐ (d) 62.8 cm
4. Find the area of a circle with radius 10 m, using π ≈ 3.14.
- ☐ (a) 62.8 m^2
- ☐ (b) 314 m^2
- ☐ (c) 31.4 m^2
- ☐ (d) 100 m^2
5. If the radius of a circle is doubled, what happens to its area?
- ☐ (a) It doubles
- ☐ (b) It triples
- ☐ (c) It becomes four times as large
- ☐ (d) It stays the same
6. Find the circumference of a circle with radius 3 cm, using π ≈ 3.14. Give the number in cm.
7. Find the area of a circle with diameter 6 cm, using π ≈ 3.14. Give the number in cm^2.
8. Give the exact area of a circle with radius 7 cm, in terms of π (for example, 4π).

Answer sheet

1. 8 cm — The diameter is twice the radius: 2 × 4 = 8 cm.
2. A = πr^2 — The area of a circle is A = πr^2. The formulas πd and 2πr give the circumference.
3. 62.8 cm — C = πd = 3.14 × 20 = 62.8 cm.
4. 314 m^2 — A = πr^2 = 3.14 × 100 = 314 m^2.
5. It becomes four times as large — Area depends on r^2. Doubling r gives (2r)^2 = 4r^2, so the area is four times as large.
6. 18.84 cm — C = 2πr = 2 × 3.14 × 3 = 18.84 cm.
7. 28.26 cm^2 — The radius is 3 cm, so A = 3.14 × 3^2 = 3.14 × 9 = 28.26 cm^2.
8. 49π cm^2 — A = πr^2 = π × 7^2 = 49π cm^2.