Question

find the volume of a right circular cone that has a height of 11.9 in and a base with a radius of 14 in. round your answer to the nearest tenth of a cubic inch.

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 $r = 14$ in and $h=11.9$ in. Substitute into the formula: $V=\frac{1}{3}\times\pi\times(14)^{2}\times11.9$.
First, calculate $(14)^{2}=196$. Then $V=\frac{1}{3}\times\pi\times196\times11.9$.
$196\times11.9 = 2332.4$. So $V=\frac{1}{3}\times\pi\times2332.4$.
$V=\frac{2332.4\pi}{3}\approx\frac{2332.4\times3.14159}{3}$.
$2332.4\times3.14159 = 7327.247416$.
$V=\frac{7327.247416}{3}\approx2442.4$.

Answer:

$2442.4$ in$^{3}$