Question

The volume of a cylinder is 60 cm'. What is the volume of a cone that shares the same radius and height as the cylinder?
(1 point)
• 20 cm3
• 40 cm3
• 90 cm3
180 cm'

Answer 1

The volume of a cylinder is given by the formula:

\[
V_{cylinder} = \pi r^2 h
\]

The volume of a cone is given by the formula:

\[
V_{cone} = \frac{1}{3} \pi r^2 h
\]

Since the cone shares the same radius and height as the cylinder, we can express the volume of the cone in terms of the volume of the cylinder.

We know:

\[
V_{cone} = \frac{1}{3} V_{cylinder}
\]

Given that the volume of the cylinder is 60 cm³, we can calculate the volume of the cone:

\[
V_{cone} = \frac{1}{3} \times 60 \text{ cm}^3 = 20 \text{ cm}^3
\]

So, the volume of the cone that shares the same radius and height as the cylinder is **20 cm³**.