Question

What is the volume, in cubic inches, of a cone with a diameter of 6 inches and a height of 7 inches? Use 3.14 for pi. Round your answer to the nearest hundredth.
cubic inches

Answer 1

To find 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, and \( h \) is the height.

1. First, we need to determine the radius. The diameter of the cone is given as 6 inches, so the radius \( r \) is:

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

2. The height \( h \) of the cone is given as 7 inches.

3. Now we can substitute the values into the volume formula. Using \( \pi \approx 3.14 \):

\[
V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7
\]

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

\[
(3)^2 = 9
\]

5. Now substitute that back into the formula:

\[
V = \frac{1}{3} \times 3.14 \times 9 \times 7
\]

6. Now calculate \( 9 \times 7 \):

\[
9 \times 7 = 63
\]

7. Substitute that into the formula:

\[
V = \frac{1}{3} \times 3.14 \times 63
\]

8. Now, calculate \( 3.14 \times 63 \):

\[
3.14 \times 63 = 197.82
\]

9. Finally, divide by 3:

\[
V = \frac{197.82}{3} \approx 65.94
\]

Thus, the volume of the cone, rounded to the nearest hundredth, is:

\[
\boxed{65.94} \text{ cubic inches}
\]