Question

What is the area of the base of the cone below?

A cone with height 12 feet and volume 90 feet cubed.
2.5 feet squared
4 feet squared
22.5 feet squared
26 feet squared

Answer 1

To find the area of the base of the cone, we can use the formula for the volume of a cone, which is given by:

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

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

Given:
- Volume \( V = 90 \) cubic feet,
- Height \( h = 12 \) feet.

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

\[
90 = \frac{1}{3} \pi r^2 (12)
\]

First, simplify the equation:

\[
90 = 4 \pi r^2
\]

Now, solve for \( r^2 \):

\[
r^2 = \frac{90}{4\pi}
\]
\[
r^2 = \frac{90}{4 \times 3.14} \quad (\text{using } \pi \approx 3.14)
\]
\[
r^2 = \frac{90}{12.56} \approx 7.15
\]

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

\[
A = \pi r^2 = \pi \times 7.15 \approx 22.45 \quad \text{(using } \pi \approx 3.14)
\]

Rounding this value gives approximately \( 22.5 \) square feet.

Therefore, the area of the base of the cone is:

\[
\boxed{22.5} \text{ feet squared}
\]