Hemisphere Practice Problems

Formulas you need

• Volume: $V = \tfrac{2}{3}\pi r^3$
• Curved surface: $2\pi r^2$
• Total surface area: $SA = 3\pi r^2$

where r = radius, V = volume, SA = total 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 hemisphere has radius r = 4. Find the volume (V).

   Answer & working

   134.04 units³

   V = 2⁄3 πr³ = 2⁄3 · π · 4³ = 128π/3 ≈ 134.04

2. A hemisphere has radius r = 3. Find the curved surface (CSA).

   Answer & working

   56.55 units²

   curved SA = 2πr² = 18π ≈ 56.55

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

   Answer & working

   150.8 units²

   total SA = 3πr² = 3 · π · 4² = 48π ≈ 150.8

4. A hemisphere has radius r = 2. Find the volume (V).

   Answer & working

   16.76 units³

   V = 2⁄3 πr³ = 2⁄3 · π · 2³ = 16π/3 ≈ 16.76

5. A hemisphere has radius r = 2. Find the curved surface (CSA).

   Answer & working

   25.13 units²

   curved SA = 2πr² = 8π ≈ 25.13

Core practice

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

   Answer & working

   261.8 units³

   V = 2⁄3 πr³ = 2⁄3 · π · 5³ = 250π/3 ≈ 261.8

2. A hemisphere has radius r = 5. Find the curved surface (CSA).

   Answer & working

   157.08 units²

   curved SA = 2πr² = 50π ≈ 157.08

3. A hemisphere has radius r = 7. Find the total surface area (SA).

   Answer & working

   461.81 units²

   total SA = 3πr² = 3 · π · 7² = 147π ≈ 461.81

4. A hemisphere has radius r = 7. Find the volume (V).

   Answer & working

   718.38 units³

   V = 2⁄3 πr³ = 2⁄3 · π · 7³ = 686π/3 ≈ 718.38

5. A hemisphere has radius r = 8. Find the curved surface (CSA).

   Answer & working

   402.12 units²

   curved SA = 2πr² = 128π ≈ 402.12

Stretch

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

   Answer & working

   32.72 units³

   V = 2⁄3 πr³ = 2⁄3 · π · 2.5³ = 10.4167π ≈ 32.72

2. A hemisphere has radius r = 3.5. Find the curved surface (CSA).

   Answer & working

   76.97 units²

   curved SA = 2πr² = 24.5π ≈ 76.97

3. A hemisphere has radius r = 5.5. Find the total surface area (SA).

   Answer & working

   285.1 units²

   total SA = 3πr² = 3 · π · 5.5² = 90.75π ≈ 285.1

4. A hemisphere has radius r = 7.5. Find the volume (V).

   Answer & working

   883.57 units³

   V = 2⁄3 πr³ = 2⁄3 · π · 7.5³ = 281.25π ≈ 883.57

5. A hemisphere has radius r = 7.5. Find the curved surface (CSA).

   Answer & working

   353.43 units²

   curved SA = 2πr² = 112.5π ≈ 353.43