Question

the volume of this cone is 2,990.88768 cubic centimeters. what is the height of this cone? round your answer to the nearest hundredth. 13.2 cm h ≈ centimeters

Explanation:

Step1: Recall volume formula for cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We know $V = 2990.88768$ cubic - centimeters and $r=13.2$ cm.

Step2: Rearrange formula for height

First, we can rewrite the volume formula to solve for $h$: $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 2990.88768$, $r = 13.2$ and $\pi\approx3.14$ into the formula:
\[

$$\begin{align*} h&=\frac{3\times2990.88768}{3.14\times(13.2)^{2}}\\ &=\frac{8972.66304}{3.14\times174.24}\\ &=\frac{8972.66304}{547.1136}\\ &\approx16.40 \end{align*}$$

\]

Answer:

$16.40$