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Year 10 Mathematics · Surface area and volume of prisms and cylinders

Name: ______________________

Date: ____________

1. Which formula gives the volume of a cylinder?
- ☐ (a) 2πrh
- ☐ (b) πr²h
- ☐ (c) πr²
- ☐ (d) 2πr² + 2πrh
2. What is the surface area of a cube with sides of 4 cm?
- ☐ (a) 64 cm²
- ☐ (b) 96 cm²
- ☐ (c) 16 cm²
- ☐ (d) 48 cm²
3. A prism has a cross-section area of 15 cm² and a length of 8 cm. What is its volume?
- ☐ (a) 23 cm³
- ☐ (b) 120 cm³
- ☐ (c) 120 cm²
- ☐ (d) 60 cm³
4. Which formula gives the surface area of a cylinder with no lid?
- ☐ (a) 2πr² + 2πrh
- ☐ (b) πr² + 2πrh
- ☐ (c) πr²h
- ☐ (d) 2πrh
5. Find the surface area of a rectangular prism 6 cm long, 2 cm wide and 5 cm high.
6. Find the volume of a cylinder with radius 5 cm and height 8 cm, correct to 1 decimal place. Use the π button.
7. Find the curved surface area of a cylinder with radius 2 cm and height 7 cm, correct to 1 decimal place.
8. A cylindrical water tank has radius 0.5 m and height 1.2 m. How many litres does it hold, to the nearest litre?

Answer sheet

1. πr²h — Volume = area of the circular cross-section (πr²) × height.
2. 96 cm² — A cube has 6 faces, each 4 × 4 = 16 cm². 6 × 16 = 96 cm². (64 is the volume in cm³.)
3. 120 cm³ — V = 15 × 8 = 120 cm³. Volume uses cubic units.
4. πr² + 2πrh — There is only one circle (the base) plus the curved surface: πr² + 2πrh.
5. 104 cm² — 2(6 × 2 + 6 × 5 + 2 × 5) = 2(12 + 30 + 10) = 2 × 52 = 104 cm².
6. 628.3 cm³ — V = π × 5² × 8 = 200π ≈ 628.3 cm³.
7. 88.0 cm² — Curved surface = 2πrh = 2 × π × 2 × 7 = 28π ≈ 87.96, which is 88.0 cm² to 1 decimal place.
8. 942 L — V = π × 0.5² × 1.2 = 0.3π ≈ 0.9425 m³. 1 m³ = 1000 L, so it holds about 942 L.