Sphere Practice Problems

Formulas you need

• Volume: $V = \tfrac{4}{3}\pi r^3$
• Surface area: $SA = 4\pi r^2$

where r = radius, V = volume, SA = surface area

Generate a new problem

Pick a difficulty, work it out, then check your answer. Every press gives a new question — the numbers are drawn fresh each time, so you can keep going.

Warm-up

1. A sphere has radius r = 4. Find the volume (V).

   Answer & working

   268.08 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 4³ = 256π/3 ≈ 268.08

2. A sphere has radius r = 2. Find the surface area (SA).

   Answer & working

   50.27 units²

   SA = 4πr² = 4 · π · 2² = 16π ≈ 50.27

3. A sphere has radius r = 1. Find the volume (V).

   Answer & working

   4.19 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 1³ = 4π/3 ≈ 4.19

4. A sphere has radius r = 3. Find the surface area (SA).

   Answer & working

   113.1 units²

   SA = 4πr² = 4 · π · 3² = 36π ≈ 113.1

5. A sphere has radius r = 3. Find the volume (V).

   Answer & working

   113.1 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 3³ = 36π ≈ 113.1

Core practice

1. A sphere has radius r = 5. Find the volume (V).

   Answer & working

   523.6 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 5³ = 500π/3 ≈ 523.6

2. A sphere has radius r = 6. Find the surface area (SA).

   Answer & working

   452.39 units²

   SA = 4πr² = 4 · π · 6² = 144π ≈ 452.39

3. A sphere has radius r = 7. Find the volume (V).

   Answer & working

   1436.76 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 7³ = 1372π/3 ≈ 1436.76

4. A sphere has radius r = 8. Find the surface area (SA).

   Answer & working

   804.25 units²

   SA = 4πr² = 4 · π · 8² = 256π ≈ 804.25

5. A sphere has radius r = 6. Find the volume (V).

   Answer & working

   904.78 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 6³ = 288π ≈ 904.78

Stretch

1. A sphere has radius r = 2.5. Find the volume (V).

   Answer & working

   65.45 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 2.5³ = 20.8333π ≈ 65.45

2. A sphere has radius r = 7.5. Find the surface area (SA).

   Answer & working

   706.86 units²

   SA = 4πr² = 4 · π · 7.5² = 225π ≈ 706.86

3. A sphere has radius r = 3.5. Find the volume (V).

   Answer & working

   179.59 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 3.5³ = 57.1667π ≈ 179.59

4. A sphere has radius r = 5.5. Find the surface area (SA).

   Answer & working

   380.13 units²

   SA = 4πr² = 4 · π · 5.5² = 121π ≈ 380.13

5. A sphere has radius r = 7.5. Find the volume (V).

   Answer & working

   1767.15 units³

   V = 4⁄3 πr³ = 4⁄3 · π · 7.5³ = 562.5π ≈ 1767.15