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

20 cm3
20 cm cubed

180 cm3
180 cm cubed

90 cm3
90 cm cubed

40 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 the volumes of both shapes.

1. The volume of a cylinder is given by the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
2. The volume of a cone is given by the formula:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]

Since the volume of the cylinder is given as 60 cm³, we can express this as:
\[
V_{\text{cylinder}} = 60 \text{ cm}^3 = \pi r^2 h
\]

Now, we can find the volume of the cone:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} V_{\text{cylinder}} = \frac{1}{3} \times 60 \text{ cm}^3 = 20 \text{ cm}^3
\]

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