Question

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

40 cm3
40 cm cubed

20 cm3
20 cm cubed

90 cm3
90 cm cubed

180 cm3

Answer 1

To find the volume of a cone that shares the same radius and height as a cylinder, we can use the formulas for their volumes:

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

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

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

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

Given that the volume of the cylinder is \( V_{\text{cylinder}} = 60 \, \text{cm}^3 \), we can substitute into the formula for the cone.

Since the cone's volume is one-third that of the cylinder, we can calculate:

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

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