Question

A)
A cone and a cylinder have the same base radius and the same height. If the volume of the cone
is 11\(\pi\) cubic units, what is the volume of the cylinder?
(1 point)
\(\frac{11}{3}\pi\ cubic\ units\)
\(14\pi\ cubic\ units\)
\(30\pi\ cubic\ units\)
\(33\pi\ cubic\ units\)

Answer 1

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

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

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

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

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

Since the cone and the cylinder have the same base radius \( r \) and height \( h \), the volume of the cylinder can be related to the volume of the cone.

From the volume of the cone, we have:

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

Multiplying both sides by 3 to isolate \( \pi r^2 h \):

\[
\pi r^2 h = 33\pi
\]

Thus, the volume of the cylinder is:

\[
V_{cylinder} = \pi r^2 h = 33\pi \text{ cubic units}
\]

So the volume of the cylinder is \( 33\pi \) cubic units.