Question

Find the volume, in cubic inches, of a cone with a radius of
13 inches and a height of 27 inches.
*Hint: Don't forget to use your Desmos calculator and STAAR
Reference Sheet to help!
Remember to use the symbol on your Desmos calculator.
(1 point)
π
4778.36 cubic inches
176.98 cubic inches
14,335.09 cubic inches
1521 cubic inches

Answer 1

To find the volume of a cone, we can use the formula:

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

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given:
- Radius \( r = 13 \) inches
- Height \( h = 27 \) inches

We can substitute these values into the formula:

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

Calculating \( 13^2 \):

\[
13^2 = 169
\]

Now substitute this value into the volume formula:

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

Now multiply \( 169 \) by \( 27 \):

\[
169 \times 27 = 4563
\]

Now substitute this back into the volume formula:

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

Calculating \( \frac{1}{3} \times 4563 \):

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

Now include \(\pi\):

\[
V = 1521\pi
\]

Using the approximate value of \(\pi \approx 3.14159\):

\[
V \approx 1521 \times 3.14159 \approx 4778.36 \text{ cubic inches}
\]

Thus, the volume of the cone is approximately **4778.36 cubic inches**, which corresponds to the first option.