Question

Consider this cylinder with known measures.

A cylinder with height 16.5 meters and volume = 594 pi meters cubed.

What is the area of the base of the cyclinder?
18 pi meters squared
36 pi meters squared
321.75 pi meters squared
9801 pi meters squared

Answer 1

To find the area of the base of the cylinder, we can use the formula for the volume of a cylinder:

\[
V = \text{Base Area} \times \text{Height}
\]

We're given the volume \( V = 594 \pi \) cubic meters and the height \( h = 16.5 \) meters.

We can rearrange the equation to find the base area:

\[
\text{Base Area} = \frac{V}{h}
\]

Substituting the known values:

\[
\text{Base Area} = \frac{594 \pi}{16.5}
\]

Now, performing the division:

\[
\text{Base Area} = \frac{594}{16.5} \pi
\]

Calculating \( \frac{594}{16.5} \):

\[
\frac{594}{16.5} = 36
\]

Thus, the base area is:

\[
\text{Base Area} = 36 \pi \text{ meters squared}
\]

So, the area of the base of the cylinder is \( 36 \pi \) meters squared.

The correct answer is:

**36 pi meters squared**.