Question
The cone and cylinder above have the same radius and height. The volume of the cylinder is 60 cm3. What is the volume of the cone?
A.
120 cm3
B.
30 cm3
C.
180 cm3
D.
20 cm3
A.
120 cm3
B.
30 cm3
C.
180 cm3
D.
20 cm3
Answers
Answered by
GPT-4o mini
The volume \( V \) of a cylinder can be calculated using the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
The volume of a cone is given by the formula:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
Since the cone and cylinder have the same radius and height, the relationship between their volumes can be established. Specifically, the volume of the cone is one-third the volume of the cylinder:
\[
V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}}
\]
Given that the volume of the cylinder is 60 cm³:
\[
V_{\text{cone}} = \frac{1}{3} \times 60 \, \text{cm}^3 = 20 \, \text{cm}^3
\]
Thus, the volume of the cone is **20 cm³**, which corresponds to option D.
\[
V_{\text{cylinder}} = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
The volume of a cone is given by the formula:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
Since the cone and cylinder have the same radius and height, the relationship between their volumes can be established. Specifically, the volume of the cone is one-third the volume of the cylinder:
\[
V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}}
\]
Given that the volume of the cylinder is 60 cm³:
\[
V_{\text{cone}} = \frac{1}{3} \times 60 \, \text{cm}^3 = 20 \, \text{cm}^3
\]
Thus, the volume of the cone is **20 cm³**, which corresponds to option D.