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

33π
cubic units
33 pi cubic units

30π
cubic units
30 pi cubic units

13π
cubic units
13 pi cubic units

3.33π
cubic units

po

Answer 1

The volume \( V \) of a cone is given by the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

The volume \( V \) of a cylinder is given by the formula:

\[
V = \pi r^2 h
\]

In this case, you are told that the cone has a volume of \( 10\pi \) cubic units. Using the cone's volume formula:

\[
10\pi = \frac{1}{3} \pi r^2 h
\]

To find the volume of the cylinder, we can relate the volumes as follows:

\[
\text{Volume of cylinder} = 3 \times \text{Volume of cone}
\]

\[
\text{Volume of cylinder} = 3 \times 10\pi = 30\pi
\]

Therefore, the volume of the cylinder is

\[
\boxed{30\pi} \text{ cubic units.}
\]