Question

A cylinder has a volume of 140 pi cubic meters and a height of 14 meters. What is the area of the base?
10 pi square meters
12 pi square meters
126 pi square meters
1,960 pi square meters

Answer 1

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

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

Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height

Given:
- Volume \( V = 140\pi \) cubic meters
- Height \( h = 14 \) meters

We can rearrange the volume formula to solve for the area of the base \( A \), where the area of the base \( A \) is equal to \( \pi r^2 \):

\[
\pi r^2 = V / h
\]

Substituting the known values:

\[
\pi r^2 = \frac{140\pi}{14}
\]

This simplifies to:

\[
\pi r^2 = 10\pi
\]

Now, to find the area of the base \( A \):

\[
A = \pi r^2 = 10\pi
\]

So, the area of the base is:

\[
\boxed{10\pi} \text{ square meters}
\]