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
90 cm3
90 cm cubed
20 cm3
20 cm cubed
40 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
90 cm3
90 cm cubed
20 cm3
20 cm cubed
40 cm3
Answers
GPT-4o mini
The volume \( V \) of a cylinder can be calculated using the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
The volume \( V \) of a cone that shares the same radius \( r \) and height \( h \) can be calculated using the formula:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
Since the volume of the cylinder is given as \( 60 \, \text{cm}^3 \), we know:
\[
\pi r^2 h = 60 \text{ cm}^3
\]
Now, for the cone:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 60 \text{ cm}^3 = 20 \text{ cm}^3
\]
Thus, the volume of the cone is **20 cm³**.
\[
V_{\text{cylinder}} = \pi r^2 h
\]
The volume \( V \) of a cone that shares the same radius \( r \) and height \( h \) can be calculated using the formula:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
Since the volume of the cylinder is given as \( 60 \, \text{cm}^3 \), we know:
\[
\pi r^2 h = 60 \text{ cm}^3
\]
Now, for the cone:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 60 \text{ cm}^3 = 20 \text{ cm}^3
\]
Thus, the volume of the cone is **20 cm³**.