Question

the volume of this cone is 12,139.554 cubic feet. what is the height of this cone? round your answer to the nearest hundredth. 21 ft h ≈ feet

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$. We know $V = 12139.554$ cubic - feet and $r = 21$ feet.

Step2: Rearrange the formula for h

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can solve for $h$. First, multiply both sides by 3 to get $3V=\pi r^{2}h$. Then, divide both sides by $\pi r^{2}$: $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute the values

Substitute $V = 12139.554$, $r = 21$, and $\pi\approx3.14$ into the formula for $h$.
$h=\frac{3\times12139.554}{3.14\times21^{2}}$.
First, calculate $21^{2}=441$ and $3\times12139.554 = 36418.662$. Then, $3.14\times441 = 1384.74$.
So, $h=\frac{36418.662}{1384.74}$.

Step4: Calculate the value of h

$h=\frac{36418.662}{1384.74}\approx26.30$.

Answer:

$26.30$ feet