Question

8 ft. height
6 ft. width

What is the volume of the cone in the image? Round the volume to the nearest cubic foot, and use 3.14 for the value of pi.

The volume of the cone is __ cubic feet.

Answer 1

To calculate the volume of a cone, you can use the formula:

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

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

From the information provided:
- The height \( h \) is 8 ft.
- The width of the cone is given as 6 ft, which means the diameter is 6 ft. Thus, the radius \( r \) is half of the diameter:

\[
r = \frac{6}{2} = 3 \text{ ft}
\]

Now plug the values of \( r \) and \( h \) into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times (3)^2 \times 8
\]

First, calculate \( (3)^2 \):

\[
(3)^2 = 9
\]

Now substitute this value back into the formula:

\[
V = \frac{1}{3} \times 3.14 \times 9 \times 8
\]

Next, calculate \( 9 \times 8 \):

\[
9 \times 8 = 72
\]

Now the volume formula looks like this:

\[
V = \frac{1}{3} \times 3.14 \times 72
\]

Calculate \( 3.14 \times 72 \):

\[
3.14 \times 72 = 226.08
\]

Now divide by 3:

\[
V = \frac{226.08}{3} = 75.36
\]

Rounding \( 75.36 \) to the nearest cubic foot gives:

\[
V \approx 75 \text{ cubic feet}
\]

Thus, the volume of the cone is **75 cubic feet**.