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

180 cm3
180 cm cubed

20 cm3
20 cm cubed

90 cm3
90 cm cubed

40 cm3

Answer 1

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

\[
V = \pi r^2 h
\]

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

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

Since the cone and the cylinder share the same radius \( r \) and height \( h \), we can relate their volumes. Given that the volume of the cylinder is 60 cm³, we can find the volume of the cone using the relationship:

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

Substituting the given volume of the cylinder:

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

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