Cylinder Practice Problems

Formulas you need

• Volume: $V = \pi r^2 h$
• Lateral surface: $LSA = 2\pi r h$
• Surface area: $SA = 2\pi r(r + h)$

where r = base radius, h = height, 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 cylinder has radius r = 4 and height h = 4. Find the volume (V).

   Answer & working

   201.06 units³

   V = πr²h = π · 4² · 4 = 64π ≈ 201.06

2. A cylinder has radius r = 2 and height h = 1. Find the lateral surface (LSA).

   Answer & working

   12.57 units²

   LSA = 2πrh = 2π · 2 · 1 = 4π ≈ 12.57

3. A cylinder has radius r = 4 and height h = 3. Find the surface area (SA).

   Answer & working

   175.93 units²

   SA = 2πr(r + h) = 2π · 4(4 + 3) = 56π ≈ 175.93

4. A cylinder has radius r = 4 and height h = 1. Find the volume (V).

   Answer & working

   50.27 units³

   V = πr²h = π · 4² · 1 = 16π ≈ 50.27

5. A cylinder has radius r = 3 and height h = 4. Find the lateral surface (LSA).

   Answer & working

   75.4 units²

   LSA = 2πrh = 2π · 3 · 4 = 24π ≈ 75.4

Core practice

1. A cylinder has radius r = 6 and height h = 3. Find the volume (V).

   Answer & working

   339.29 units³

   V = πr²h = π · 6² · 3 = 108π ≈ 339.29

2. A cylinder has radius r = 8 and height h = 10. Find the lateral surface (LSA).

   Answer & working

   502.65 units²

   LSA = 2πrh = 2π · 8 · 10 = 160π ≈ 502.65

3. A cylinder has radius r = 6 and height h = 8. Find the surface area (SA).

   Answer & working

   527.79 units²

   SA = 2πr(r + h) = 2π · 6(6 + 8) = 168π ≈ 527.79

4. A cylinder has radius r = 7 and height h = 6. Find the volume (V).

   Answer & working

   923.63 units³

   V = πr²h = π · 7² · 6 = 294π ≈ 923.63

5. A cylinder has radius r = 8 and height h = 5. Find the lateral surface (LSA).

   Answer & working

   251.33 units²

   LSA = 2πrh = 2π · 8 · 5 = 80π ≈ 251.33

Stretch

1. A cylinder has radius r = 1.5 and height h = 9.5. Find the volume (V).

   Answer & working

   67.15 units³

   V = πr²h = π · 1.5² · 9.5 = 21.375π ≈ 67.15

2. A cylinder has radius r = 6.5 and height h = 11.5. Find the lateral surface (LSA).

   Answer & working

   469.67 units²

   LSA = 2πrh = 2π · 6.5 · 11.5 = 149.5π ≈ 469.67

3. A cylinder has radius r = 3.5 and height h = 12. Find the surface area (SA).

   Answer & working

   340.86 units²

   SA = 2πr(r + h) = 2π · 3.5(3.5 + 12) = 108.5π ≈ 340.86

4. A cylinder has radius r = 6.5 and height h = 6.5. Find the volume (V).

   Answer & working

   862.76 units³

   V = πr²h = π · 6.5² · 6.5 = 274.625π ≈ 862.76

5. A cylinder has radius r = 5.5 and height h = 2.5. Find the lateral surface (LSA).

   Answer & working

   86.39 units²

   LSA = 2πrh = 2π · 5.5 · 2.5 = 27.5π ≈ 86.39