Question

a cylinder and a cone have the same radius and the same volume. the height of the cone is 18 cm. what is the height of the cylinder

Answer 1

the height of the cylinder is 6 cm.

Explanation:

Let's start by using the formulas for the volume of a cylinder and a cone:

Volume of a cylinder = πr^2h

Volume of a cone = (1/3)πr^2h

Given that the cylinder and cone have the same radius and volume, we can set their volume equations equal to each other:

πr^2h = (1/3)πr^2(18)

Simplifying this equation by canceling out πr^2 on both sides, we get:

h = (1/3) * 18

h = 6

Therefore, the height of the cylinder is 6 cm.2