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Year 10 Maths — Combined solids

Find the surface area and volume of a solid made by joining a cylinder, a cone or a hemisphere.

Name: ________________________

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

  2. 2.Sort each formula by what it measures.

    Groups: A surface area · A volume

    • πrl
    • 4/3 πr³
    • 1/3 πr²h
    • 2πrh
    • 3πr²
    • πr²h

  3. 3.A toy is a cone standing on a hemisphere, both of radius 7 cm. The cone is 24 cm tall. What is the cone's slant height, in centimetres?

  4. 4.A cone, a hemisphere and a cylinder all have a radius of 7 cm, and the cone and the cylinder are both 7 cm tall. Which holds the most?

    • a) The hemisphere
    • b) The cone
    • c) The cylinder
    • d) They all hold the same

  5. 5.Match each solid to the formula for its curved surface area.

    • A sphere
    • A hemisphere
    • A cone
    • A cylinder
    • 2πrh
    • πrl
    • 2πr²
    • 4πr²

  6. 6.A sphere of radius 7 cm is cut exactly in half. Take π = 22/7. What is the total surface area of one hemisphere, counting its flat face, in square centimetres?

  7. 7.A cylinder of radius 7 cm and height 10 cm has a cone of radius 7 cm and slant height 25 cm standing on top of it. Its outside is the cone's curved surface, the cylinder's curved surface and the circular base. Take π = 22/7. What is the total surface area, in square centimetres?

  8. 8.A solid is a cylinder of radius 7 cm and height 10 cm with a cone of radius 7 cm and height 12 cm standing on top of it. Take π = 22/7. What is the volume of the cylinder part, in cubic centimetres?

Answer key — Year 10 Maths — Combined solids

  1. 1. 308
  2. 2. 2πrh → A surface area; πr²h → A volume; 4/3 πr³ → A volume; πrl → A surface area; 3πr² → A surface area; 1/3 πr²h → A volume
  3. 3. 25
  4. 4. c) The cylinder
  5. 5. A sphere → 4πr²; A hemisphere → 2πr²; A cone → πrl; A cylinder → 2πrh
  6. 6. 462
  7. 7. 1144
  8. 8. 1540