Solid geometry

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. A cylinder of radius 4 is sliced by a plane parallel to its base. What shape is the cross section?
    1. A circle of radius 4
    2. A rectangle
    3. An ellipse
  2. A 9 by 6 rectangle is rotated about one of its sides. Which solid does it sweep out?
    1. A cylinder
    2. A cone
    3. A sphere
  3. A cone of height 3 is sliced by a vertical plane through its apex. What shape is the cross section?
    1. An isosceles triangle
    2. A circle
    3. A rectangle
  4. A solid has volume 25 cm³. It is enlarged with scale factor 2. Find the new volume.
  5. A solid has surface area 49 cm². It is enlarged with scale factor 3. Find the new surface area.
  6. Two similar solids have volumes in the ratio 27:127 : 1. Find the ratio of their heights (scale factor).
  7. Find the volume of a cylinder with radius 3 cm and height 4 cm (exact, in terms of π).Not to scale
  8. A prism has a triangular base with base 2 cm and height 7 cm, and the prism is 7 cm long. Find its volume (cm³).Not to scale
  9. A cylinder of radius 5 cm has volume 175π175\pi cm³. Find its height (cm).Not to scale
  10. Find the volume of a cone with radius 6 cm and height 6 cm (exact, in terms of π).Not to scale
  11. A pyramid has a square base of side 4 m and height 15 m. Find its volume (m³).Not to scale
  12. A cone and a cylinder have the same radius 5 and the same height. What fraction of the cylinder's volume is the cone's?