Question

the volume of this cone is 23,150.592 cubic inches. what is the height of this cone? round your answer to the nearest hundredth. 24 in h ≈ inches

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. Given $V=23150.592$ cubic - inches and $r = 24$ inches.

Step2: Rearrange formula for height

We can rewrite the formula for $h$ as $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 23150.592$, $r = 24$ into the formula:
\[

$$\begin{align*} h&=\frac{3\times23150.592}{\pi\times(24)^{2}}\\ &=\frac{69451.776}{\pi\times576}\\ &=\frac{69451.776}{3.14\times576}\\ &=\frac{69451.776}{1808.64}\\ &= 38.4 \end{align*}$$

\]

Answer:

$38.40$ inches