Find the volume of a right circular cone that has a height of 17.5 m and a base with a circumference of 19.4 m. Round your answer to the nearest tenth of a cubic meter.

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 ($h$) = 17.5 m
• Circumference of the base = 19.4 m

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:

$r = \frac{19.4}{2 \pi}$

$r \approx \frac{19.4}{6.2832}$

$r \approx 3.1 \, \text{m}$

Now, we can use the radius to find the volume of the cone:

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

Substitute the values of $r$ and $h$:

$V = \frac{1}{3} \pi (3.1)^2 (17.5)$

$V = \frac{1}{3} \pi (9.61) (17.5)$

$V = \frac{1}{3} \pi (168.175)$

$V \approx \frac{1}{3} (528.3)$

$V \approx 176.1 \, \text{m}^3$

Therefore, the volume of the right circular cone is approximately 176.1 cubic meters.