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Grade 10 · Measurement
Measurement: Surface Area, Volume & Scaling (Grade 10)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    A cube has a volume of 216 cm3. Determine the length of one edge, and hence the total surface area of the cube.
    (4)
  2. 2
    The diagram below shows a cylinder. Calculate its volume. (π ≈ 3,14)
    (3)
    r = 5 cm h = 12 cm
  3. 3
    The diagram below shows a cone. Calculate its volume. (π ≈ 3,14)
    (3)
    r = 3 cm h = 4 cm
  4. 4
    Calculate the volume of the sphere in the diagram below. (π ≈ 3,14)
    (3)
    r = 3 cm
  5. 5
    Calculate the surface area of the sphere in the diagram below. (π ≈ 3,14)
    (3)
    r = 6 cm
  6. 6
    The diagram below shows a pyramid. Calculate its volume.
    (3)
    h = 9 cm base area 30 cm²
  7. 7
    The diagram below shows a right pyramid with a square base of side 18 cm and a perpendicular height of 12 cm. Calculate the slant height ℓ and the total surface area of the pyramid.
    (5)
    18 cmh = 12 cmℓ
  8. 8
    The diagram below shows a right pyramid whose base is an equilateral triangle with sides of 8 cm. The slant height of each sloping face is 10 cm. Calculate the total surface area of the pyramid.
    (4)
    8 cmℓ = 10 cmthe base is an equilateral triangle
  9. 9
    A solid's dimensions are all doubled. What happens to its volume?
    (2)
  10. 10
    A solid's dimensions are all tripled. What happens to its surface area?
    (2)
  11. 11
    The diagram below shows a triangular prism. Calculate its volume.
    (3)
    4 cm6 cm10 cm
  12. 12
    Calculate the volume of the cylinder in the diagram below. (π ≈ 3,14)
    (3)
    r = 4 cm h = 8 cm
  13. 13
    The solid in the diagram below is a cylinder of radius 4 cm and height 10 cm with a cone of height 3 cm on top. Calculate the volume and the total surface area of the solid, correct to TWO decimal places.
    (6)
    r = 4 cm10 cm3 cm
  14. 14
    A cube with edges of 3 cm is glued to the centre of the top of a cube with edges of 6 cm, as in the diagram below. Calculate the total surface area of the solid.
    (3)
    6 cm3 cm
  15. 15
    Which two solids have a ⅓ in their volume formula?
    (1)
TOTAL: 48 marks
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