Surface area & volume

Surface area is the total area of all the outer faces of a 3D shape, while volume is the amount of space it occupies inside. For a rectangular prism, volume = length × width × height. For a cylinder, volume = π × r² × h, and surface area = 2πr² + 2πrh (the two circular ends plus the curved side). These calculations matter for real tasks like working out how much paint or water a container needs.

Key terms

Surface area:

The total area of all outer faces of a 3D shape.

Volume:

The amount of space a 3D shape occupies.

Questions

1. 1. Volume measures:

   • The space inside a 3D shape
   • The outer area only
   • The perimeter
   • The weight

2. 2. Surface area measures:

   • The total area of all outer faces
   • The space inside a shape
   • The weight of a shape
   • The colour of a shape

3. 3. A rectangular prism is 2m × 3m × 4m. What is its volume?

   • 9m³
   • 14m³
   • 24m³
   • 48m³

4. 4. Volume of a rectangular prism = length × width ×:

   • Height
   • Perimeter
   • Area
   • Diameter

5. 5. Volume is measured in:

   • Cubic units
   • Square units
   • Linear units
   • Degrees

6. 6. A cube has sides of 3cm. What is its volume?

   • 9cm³
   • 18cm³
   • 27cm³
   • 81cm³

7. 7. Surface area is measured in:

   • Square units
   • Cubic units
   • Linear units
   • Litres only

8. 8. A cylinder has radius 3cm and height 10cm. Using V = πr²h, its approximate volume is:

   • 94.2cm³
   • 188.4cm³
   • 282.6cm³
   • 30cm³

9. 9. A rectangular prism is 5m × 2m × 3m. What is its volume?

   • 10m³
   • 20m³
   • 30m³
   • 40m³

10. 10. A box needs to hold 100 items each 1m³. What minimum volume must the box have?

    • 10m³
    • 50m³
    • 100m³
    • 1,000m³

11. 11. A cylinder has radius 2m and height 5m. Using V = πr²h, its approximate volume is:

    • 31.4m³
    • 62.8m³
    • 125.6m³
    • 15.7m³

12. 12. The surface area of a rectangular prism includes:

    • All six faces
    • Only the top
    • Only the base
    • Just one side

13. 13. A cube has a volume of 64cm³. What is the length of one side?

    • 2cm
    • 4cm
    • 6cm
    • 8cm

14. 14. A cylinder's surface area formula, 2πr² + 2πrh, accounts for:

    • The two circular ends plus the curved side
    • Only the circular ends
    • Only the curved side
    • The volume, not surface area

15. 15. A cylindrical tank has radius 2m and height 5m. Using V = πr²h, its approximate volume is:

    • 31.4m³
    • 62.8m³
    • 78.5m³
    • 125.6m³

16. 16. Using the same tank (radius 2m, height 5m), its approximate surface area (2πr² + 2πrh) is:

    • 62.8m²
    • 75.4m²
    • 87.9m²
    • 100.5m²

17. 17. A swimming pool is 10m long, 5m wide, and 1.5m deep. How many litres of water does it hold? (1m³ = 1,000L)

    • 7,500L
    • 15,000L
    • 75,000L
    • 750,000L

18. 18. Doubling the radius of a cylinder (keeping height the same) causes its volume to:

    • Quadruple (×4)
    • Double (×2)
    • Stay the same
    • Triple (×3)

19. 19. A cereal box (rectangular prism) is 8cm × 20cm × 30cm. How much cardboard (surface area) is needed to make it?

    • 1,520cm²
    • 1,760cm²
    • 2,080cm²
    • 4,800cm²

20. 20. A can of soup has radius 4cm and height 12cm. Approximately how much metal (surface area) is needed to make it? (2πr² + 2πrh)

    • 301.6cm²
    • 402.1cm²
    • 150.8cm²
    • 201.1cm²

21. 21. A water tank needs to hold at least 50,000L. If it is cylindrical with radius 2m, approximately what minimum height (in m) is needed? (V = πr²h, 1m³ = 1,000L)

    • 2m
    • 4m
    • 6m
    • 8m