Question

the volume of this cone is 364.7424 cubic meters. what is the height of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. h = meters

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 $V = 364.7424$ cubic - meters and $r = 6.6$ m and $\pi\approx3.14$. We need to solve for $h$.

Step2: Rearrange the formula for $h$

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can get $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute the given values

Substitute $V = 364.7424$, $\pi\approx3.14$ and $r = 6.6$ into the formula for $h$.
$h=\frac{3\times364.7424}{3.14\times(6.6)^{2}}$
First, calculate $(6.6)^{2}=6.6\times6.6 = 43.56$.
Then, $3.14\times43.56 = 136.7784$.
And $3\times364.7424 = 1094.2272$.
So, $h=\frac{1094.2272}{136.7784}=8.00$.

Answer:

$8.00$