Question

The volume of a cylinder is 60 cm3
. What is the volume of a cone that shares the same radius and height as the cylinder?(1 point)
Responses

90 cm3
90 cm cubed

180 cm3
180 cm cubed

20 cm3
20 cm cubed

40 cm3

Answer 1

The volume \( V \) of a cylinder is given by the formula:

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

The volume \( V \) of a cone is given by the formula:

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

Since the cone shares the same radius \( r \) and height \( h \) as the cylinder, we can relate the two volumes.

Given that the volume of the cylinder is \( 60 \, \text{cm}^3 \), we can find the volume of the cone:

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

Substituting the volume of the cylinder:

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

So, the volume of the cone is **20 cm³**.