Question

find the volume of a right circular cone that has a height of 18.9 in and a base with a circumference of 15 in. round your answer to the nearest tenth of a cubic inch.

Explanation:

Step1: Find the radius of the base

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=15$ in, we can solve for $r$. So, $r=\frac{C}{2\pi}=\frac{15}{2\pi}$ in.

Step2: Calculate the volume of the cone

The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = \frac{15}{2\pi}$ and $h = 18.9$ into the formula.
\[

$$\begin{align*} V&=\frac{1}{3}\pi(\frac{15}{2\pi})^{2}\times18.9\\ &=\frac{1}{3}\pi\times\frac{225}{4\pi^{2}}\times18.9\\ &=\frac{225\times18.9}{12\pi}\\ &=\frac{4252.5}{12\pi}\\ &\approx112.9 \end{align*}$$

\]

Answer:

$112.9$