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

3.33π
cubic units
3.33 pi cubic units

13π
cubic units
13 pi cubic units

30π
cubic units

Answer 1

To find the volume of the cylinder, we first need to recall the formulas for the volumes of both the cone and the cylinder.

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

\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]

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

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

\[
V_{\text{cylinder}} = \pi r^2 h
\]

In this case, we know that the volume of the cone is \( 10\pi \) cubic units. Therefore:

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

By dividing both sides by \( \pi \):

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

Multiplying both sides by 3:

\[
r^2 h = 30
\]

Now we can find the volume of the cylinder using the previously established volume formula:

\[
V_{\text{cylinder}} = \pi r^2 h = \pi (r^2 h) = \pi \cdot 30 = 30\pi
\]

Thus, the volume of the cylinder is:

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