Question

a cone has a radius of 6 inches and a hight of 8 inches. what is the volume to the nearest tenth of a cubic inch of the cone?

Answer 1

To calculate the volume \( V \) of a cone, you can use the formula:

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

where \( r \) is the radius and \( h \) is the height of the cone.

Given:
- Radius \( r = 6 \) inches
- Height \( h = 8 \) inches

Substituting the values into the formula:

\[
V = \frac{1}{3} \pi (6)^2 (8)
\]

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substituting that back into the volume equation:

\[
V = \frac{1}{3} \pi (36)(8)
\]

Calculating \( 36 \times 8 \):

\[
36 \times 8 = 288
\]

Now substituting that value in:

\[
V = \frac{1}{3} \pi (288)
\]

Simplifying \( \frac{1}{3} \times 288 \):

\[
\frac{288}{3} = 96
\]

So now we have:

\[
V = 96 \pi
\]

Using \( \pi \approx 3.14159 \):

\[
V \approx 96 \times 3.14159 \approx 301.59264
\]

Rounding to the nearest tenth:

\[
V \approx 301.6
\]

Thus, the volume of the cone is approximately **301.6 cubic inches**.