Question

the volume of this cone is 147.00852 cubic meters. what is the height of this cone? round your answer to the nearest hundredth. 5.1 m h ≈ meters

Explanation:

Step1: Recall cone volume formula

The volume formula of a cone is $V = \frac{1}{3}\pi r^{2}h$, where $V$ is the volume, $r$ is the radius and $h$ is the height. We know $V=147.00852$ cubic - meters and $r = 5.1$ m. We need to solve for $h$.

Step2: Rearrange the formula for $h$

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can isolate $h$ by multiplying both sides of the equation by $3$ and then dividing by $\pi r^{2}$. So $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute the given values

Substitute $V = 147.00852$, $r = 5.1$ into the formula:
\[

$$\begin{align*} h&=\frac{3\times147.00852}{\pi\times(5.1)^{2}}\\ &=\frac{441.02556}{\pi\times26.01}\\ &=\frac{441.02556}{3.14\times26.01}\\ &=\frac{441.02556}{81.6714}\\ &\approx5.40 \end{align*}$$

\]

Answer:

$5.40$