Question

find the volume of a right circular cone that has a height of 15.8 in and a base with a diameter of 12.7 in. round your answer to the nearest tenth of a cubic inch.

Explanation:

Step1: Find the radius

The radius $r$ is half of the diameter. Given diameter $d = 12.7$ in, so $r=\frac{d}{2}=\frac{12.7}{2}=6.35$ in.

Step2: Use the cone - volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 6.35$ in and $h=15.8$ in.
$V=\frac{1}{3}\times\pi\times(6.35)^{2}\times15.8$.
First, calculate $(6.35)^{2}=6.35\times6.35 = 40.3225$.
Then, $V=\frac{1}{3}\times\pi\times40.3225\times15.8$.
$V=\frac{1}{3}\times\pi\times637.0955$.
$V=\frac{637.0955\pi}{3}\approx\frac{637.0955\times3.14159}{3}$.
$637.0955\times3.14159 = 1991.9777$.
$V=\frac{1991.9777}{3}\approx664.0$.

Answer:

$664.0$ in³