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Year 10 Maths — Surface area and volume

Find surface areas and volumes of cones, spheres and hemispheres.

Name: ________________________

  1. 1.A sphere has a radius of 7 cm. Take π = 22/7. What is its surface area, in square centimetres?

  2. 2.Which of these gives the volume of a sphere?

    • a) (4/3) × π × r × r × r
    • b) (1/3) × π × r × r × h
    • c) 4 × π × r × r
    • d) 2 × π × r × r

  3. 3.Which of these gives the volume of a cone?

    • a) π × r × l
    • b) π × r × r × h
    • c) (4/3) × π × r × r × r
    • d) (1/3) × π × r × r × h

  4. 4.A sphere has a radius of 21 cm. Take π = 22/7. What is its volume, in cubic centimetres?

  5. 5.Match each solid to the formula for its volume.

    • Cuboid
    • Cylinder
    • Cone
    • Sphere
    • π × r × r × h
    • (1/3) × π × r × r × h
    • length × width × height
    • (4/3) × π × r × r × r

  6. 6.A sphere has a radius of 14 cm. Take π = 22/7. What is its surface area, in square centimetres?

  7. 7.A cone has a radius of 7 cm and a slant height of 25 cm. Take π = 22/7. What is its curved surface area, in square centimetres?

  8. 8.A cone has a radius of 7 cm and a height of 24 cm. What is its slant height, in centimetres?

Answer key — Year 10 Maths — Surface area and volume

  1. 1. 616
  2. 2. a) (4/3) × π × r × r × r
  3. 3. d) (1/3) × π × r × r × h
  4. 4. 38808
  5. 5. Cuboid → length × width × height; Cylinder → π × r × r × h; Cone → (1/3) × π × r × r × h; Sphere → (4/3) × π × r × r × r
  6. 6. 2464
  7. 7. 550
  8. 8. 25