Question

A cone has a radius of 5.6 in and a height of 3 in. Find the volume of this cone in cubic inches. Use 3.14 for π. Round your answer to the nearest cubic inch.

Answer 1

To find the volume \( V \) of a cone, we can use the formula:

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

where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) (pi) is approximately 3.14.

For the cone given:
- The radius \( r = 5.6 \) in,
- The height \( h = 3 \) in.

Now, we can plug these values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (5.6)^2 \times 3
\]

First, we calculate \( (5.6)^2 \):

\[
(5.6)^2 = 31.36
\]

Next, we substitute this back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 31.36 \times 3
\]

Now, calculate \( 3.14 \times 31.36 \):

\[
3.14 \times 31.36 \approx 98.7504
\]

Now, multiply by 3:

\[
98.7504 \times 3 \approx 296.2512
\]

Finally, divide by 3 to obtain the volume:

\[
V \approx \frac{296.2512}{3} \approx 98.7504
\]

Rounding to the nearest cubic inch:

\[
V \approx 99 \text{ cubic inches}
\]

Thus, the volume of the cone is approximately **99 cubic inches**.