Question

Complete this assessment to review what you've learned. It will not count toward your grade. 2 of 52 of 5 Items 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.

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,
- \( h \) is the height,
- \( \pi \) is a constant (approximately 3.14).

Given the diameter of the cone is 6 inches, the radius \( r \) will be half of the diameter:

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

The height \( h \) is given as 7 inches. Now substitute \( r \), \( h \), and \( \pi \) into the volume formula:

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

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

\[
(3)^2 = 9
\]

Now substitute this back into the equation:

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

Next, calculate \( 9 \times 7 \):

\[
9 \times 7 = 63
\]

Now substitute this back into the equation:

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

Now calculate \( 3.14 \times 63 \):

\[
3.14 \times 63 = 197.82
\]

Now, divide this result by 3 to find the volume:

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

Finally, round to the nearest hundredth, so the volume of the cone is:

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