Question
A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 10π
cubic units, what is the volume of the cylinder?(1 point)
Responses
3.33π
cubic units
3.33 pi cubic units
30π
cubic units
30 pi cubic units
33π
cubic units
33 pi cubic units
13π
cubic units
cubic units, what is the volume of the cylinder?(1 point)
Responses
3.33π
cubic units
3.33 pi cubic units
30π
cubic units
30 pi cubic units
33π
cubic units
33 pi cubic units
13π
cubic units
Answers
GPT-4o mini
The volume of a cone is given by the formula:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
The volume of a cylinder is given by the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
Since the cone and the cylinder have the same base radius \( r \) and height \( h \), we can express the volume of the cylinder in terms of the volume of the cone.
Given that the volume of the cone is \( 10\pi \) cubic units:
\[
\frac{1}{3} \pi r^2 h = 10\pi
\]
To find the volume of the cylinder, we can manipulate the formula for the volume of the cone:
\[
\pi r^2 h = 3 \times (10\pi) = 30\pi
\]
So the volume of the cylinder is \( 30\pi \) cubic units.
Thus, the correct response is:
**30π cubic units**.
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
The volume of a cylinder is given by the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
Since the cone and the cylinder have the same base radius \( r \) and height \( h \), we can express the volume of the cylinder in terms of the volume of the cone.
Given that the volume of the cone is \( 10\pi \) cubic units:
\[
\frac{1}{3} \pi r^2 h = 10\pi
\]
To find the volume of the cylinder, we can manipulate the formula for the volume of the cone:
\[
\pi r^2 h = 3 \times (10\pi) = 30\pi
\]
So the volume of the cylinder is \( 30\pi \) cubic units.
Thus, the correct response is:
**30π cubic units**.