Question

Calculate the volume of the cone.

A cone 27 centimeters high with radius of 13 centimeters.

What is the volume of a cone with a height of 27 cm and a radius of 13 cm? Round your answer to the nearest tenth.

Use the button on your calculator to complete this problem.

V =

Answer 1

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

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

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

In this case, the radius \( r = 13 \) cm and the height \( h = 27 \) cm.

Now, we can plug in the values:

\[
V = \frac{1}{3} \pi (13^2)(27)
\]

First, calculate \( 13^2 \):

\[
13^2 = 169
\]

Now, substitute back into the volume formula:

\[
V = \frac{1}{3} \pi (169)(27)
\]

Next, calculate \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Now we can find the volume:

\[
V = \frac{1}{3} \pi (4563)
\]

Calculating \( \frac{4563}{3} \):

\[
\frac{4563}{3} = 1521
\]

Thus, the volume is:

\[
V \approx 1521 \pi
\]

Now, to find the numerical value, we use \( \pi \approx 3.14159 \):

\[
V \approx 1521 \times 3.14159 \approx 4777.96339
\]

Rounding to the nearest tenth:

\[
V \approx 4778.0
\]

Therefore, the volume of the cone is approximately:

\[
\boxed{4778.0} \text{ cubic centimeters}
\]