Volume of pyramids and cones

Math

Definition

The volume of a pyramid or cone is one-third the volume of the corresponding prism or cylinder with the same base and height. This reflects the fact that a pyramid or cone tapers to a point, holding exactly one-third as much space.

Examples

  • A cone with radius 3 and height 10 has volume = (1/3)π(9)(10) = 30π cubic units
  • A square pyramid with base edge 6 and height 9 has volume = (1/3)(36)(9) = 108 cubic units
  • An ice cream cone is roughly a cone shape — its volume depends on the radius of the opening and the depth
Key Fact

V = (1/3)Bh (pyramids); V = (1/3)πr²h (cones)

Related Terms

Volume of prisms and cylinders Surface area Area of polygons

Study This Concept

Practice volume of pyramids and cones with free review games in these units:

Geometry Unit 10: Area and Volume