Question

find the volume of a right circular cone that has a height of 17.8 ft and a base with a radius of 17.8 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Recall volume formula

The volume formula for a right - circular cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height.

Step2: Substitute given values

Given $r = 17.8$ ft and $h=17.8$ ft. Substitute into the formula: $V=\frac{1}{3}\pi(17.8)^{2}(17.8)$.
First, calculate $(17.8)^{2}(17.8)=(17.8)^{3}=17.8\times17.8\times17.8 = 5639.752$.
Then, $V=\frac{1}{3}\pi\times5639.752$.
Since $\pi\approx3.14159$, $V=\frac{1}{3}\times3.14159\times5639.752$.
$\frac{1}{3}\times3.14159\times5639.752 = 3.14159\times\frac{5639.752}{3}=3.14159\times1879.917333\approx5902.2$.

Answer:

$5902.2$