Math
Volume of pyramids and cones.
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
Real-world.
- 1 A cone with radius 3 and height 10 has volume = (1/3)π(9)(10) = 30π cubic units
- 2 A square pyramid with base edge 6 and height 9 has volume = (1/3)(36)(9) = 108 cubic units
- 3 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)