Find the volume of a right circular cone that has a height of 11.1 in and a base with a circumference of 17.6 in. Round your answer to the nearest tenth of a cubic inch.

To find the volume of a right circular cone, we 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 of the cone.

Given:

• Height ($h$) = 11.1 inches
• Circumference of the base = 17.6 inches

First, we need to find the radius ($r$) of the base. The circumference ($C$) of a circle is given by:

$C = 2 \pi r$

We can solve for $r$:

$r = \frac{C}{2 \pi}$

Substitute the given circumference:

$r = \frac{17.6}{2 \pi}$

$r \approx \frac{17.6}{6.2832}$

$r \approx 2.8 \text{ inches}$

Now, we can use the radius to find the volume of the cone. Substitute $r$ and $h$ into the volume formula:

$V = \frac{1}{3} \pi (2.8)^2 (11.1)$

Calculate $(2.8)^2$:

$(2.8)^2 = 7.84$

Now, substitute back into the volume formula:

$V = \frac{1}{3} \pi (7.84) (11.1)$

$V = \frac{1}{3} \pi (87.024)$

$V \approx \frac{1}{3} (273.4)$

$V \approx 91.1 \text{ cubic inches}$

So, the volume of the right circular cone is approximately 91.1 cubic inches.