Volume of pyramids, cones, and spheres

Find the volume of pyramids, cones, and spheres by substituting into the correct formula, including reverse problems that rearrange the formula to find a missing radius, height, or base length, and scale-factor questions.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

Terminology

  • pyramid
  • cone
  • sphere
  • volume
  • base area
  • perpendicular height
  • radius
  • in terms of pi
  • scale factor

Task goals

  • Find the volume of a cone, square pyramid, or rectangular pyramid using the correct formula.
  • Find the volume of a sphere or hemisphere, keeping the answer in terms of pi where appropriate.
  • Find a cone's perpendicular height from its radius and slant height using Pythagoras' theorem before finding the volume.
  • Rearrange a volume formula to solve reverse problems (given the volume, find a missing radius, height, or base side length).
  • Apply the k-cubed scale-factor rule when every length of a solid is multiplied by a constant.
  • Find the total volume of a composite solid made of two joined shapes (e.g. a hemisphere joined to a cone).

Key skills

  • Volume
  • Pyramids
  • Cones
  • And
  • Spheres

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included