Question
A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 11
π
cubic units, what is the volume of the cylinder?
(1 point)
Responses
11
3
π
c
u
b
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c
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s
11
3
π
c
u
b
i
c
u
n
i
t
s
14
π
c
u
b
i
c
u
n
i
t
s
14
π
c
u
b
i
c
u
n
i
t
s
33
π
c
u
b
i
c
u
n
i
t
s
33
π
c
u
b
i
c
u
n
i
t
s
30
π
c
u
b
i
c
u
n
i
t
s
π
cubic units, what is the volume of the cylinder?
(1 point)
Responses
11
3
π
c
u
b
i
c
u
n
i
t
s
11
3
π
c
u
b
i
c
u
n
i
t
s
14
π
c
u
b
i
c
u
n
i
t
s
14
π
c
u
b
i
c
u
n
i
t
s
33
π
c
u
b
i
c
u
n
i
t
s
33
π
c
u
b
i
c
u
n
i
t
s
30
π
c
u
b
i
c
u
n
i
t
s
Answers
GPT-4o mini
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the base radius and \( h \) is the height.
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
Since the cone and the cylinder have the same base radius \( r \) and height \( h \), we know that the volume of the cylinder will be three times that of the cone.
Given that the volume of the cone is \( 11 \pi \) cubic units, we can find the volume of the cylinder:
\[
V_{\text{cylinder}} = 3 \times V_{\text{cone}} = 3 \times 11 \pi = 33 \pi
\]
Thus, the volume of the cylinder is
\[
\boxed{33 \pi} \text{ cubic units.}
\]
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the base radius and \( h \) is the height.
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
Since the cone and the cylinder have the same base radius \( r \) and height \( h \), we know that the volume of the cylinder will be three times that of the cone.
Given that the volume of the cone is \( 11 \pi \) cubic units, we can find the volume of the cylinder:
\[
V_{\text{cylinder}} = 3 \times V_{\text{cone}} = 3 \times 11 \pi = 33 \pi
\]
Thus, the volume of the cylinder is
\[
\boxed{33 \pi} \text{ cubic units.}
\]