Question

Question
A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 10 π
cubic units, what is the volume of the cylinder?(7 points)
Responses

30π
cubic units
30pi cubic units

13π
cubic units
13pi cubic units

3.33π
cubic units
3.33pi cubic units

33π
cubic units
33pi cubic units
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Answer 1

The volume \( V \) of a cone can be calculated using the formula:

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

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

In your case, the volume of the cone is given as \( 10\pi \) cubic units.

So, we have:

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

Dividing both sides by \( \pi \):

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

Now, multiplying both sides by 3, we get:

\[
r^2 h = 30
\]

Now, let's find the volume of the cylinder, which is given by the formula:

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

Substituting \( r^2 h \) into the volume formula for the cylinder, we have:

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

Thus, the volume of the cylinder is \( \boxed{30\pi} \) cubic units.