Question

question
find the volume of a right circular cone that has a height of 9 cm and a base with a circumference of 16.9 cm. round your answer to the nearest tenth of a cubic centimeter.

Explanation:

Step1: Find the radius from the circumference.

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=16.9$ cm, we can solve for $r$: $r=\frac{C}{2\pi}=\frac{16.9}{2\pi}$ cm.

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 $r = \frac{16.9}{2\pi}$ and $h = 9$ into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\pi(\frac{16.9}{2\pi})^{2}\times9\\ &=\frac{1}{3}\pi\times\frac{16.9^{2}}{4\pi^{2}}\times9\\ &=\frac{16.9^{2}}{4\pi}\\ &=\frac{285.61}{4\pi}\approx22.7 \end{align*}$$

\]

Answer:

$22.7$ cm³