Question

A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 11π
cubic units, what is the volume of the cylinder?



(1 point)
Responses

14π cubic units
14π cubic units

113π cubic units
113π cubic units

30π cubic units
30π cubic units

33π cubic units
33π cubic units

Answer 1

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:

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

Given that the volume of the cone is \( 11\pi \) cubic units, we can set up the equation:

\[
\frac{1}{3} \pi r^2 h = 11\pi
\]

To eliminate \(\pi\) from both sides, we have:

\[
\frac{1}{3} r^2 h = 11
\]

Multiplying both sides by 3 gives:

\[
r^2 h = 33
\]

Now, substituting this relationship into the formula for the volume of the cylinder:

\[
V_{\text{cylinder}} = \pi r^2 h = \pi (r^2 h) = \pi (33) = 33\pi
\]

So, the volume of the cylinder is:

\[
\boxed{33\pi \text{ cubic units}}
\]