Question

QUESTIONING STRATEGIES

If a cone shares a base with a cylinder, and the
volume of the cylinder is given, along with the
heights of the cylinder and of the cone, how could
you find the volume of the cone?

Answer 1

cone volume = cylinder volume times 1/3 the ratio of cone height to cylinder height

Explanation:

Let h1 and V1 represent the height and volume of the cylinder, and h2 and V2 the height and volume of the cone.

We are told they have a common base area (B), so ...

V1 = Bh1 ⇒ B = V1/h1

V2 = (1/3)Bh2 = (1/3)(V1/h1)h2

The volume of the cone is ...

V2 = h2/(3h1)×V1

"one-third the ratio of cone height to cylinder height, multiplied by the cylinder volume."