Question

the volume of this cone is 489.84 cubic meters. what is the radius of this cone? round your answer to the nearest hundredth. 13 m r ≈ 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 $V = 489.84$ cubic - meters and $h=13$ meters.

Step2: Rearrange formula to solve for $r$

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can first multiply both sides by $3$ to get $3V=\pi r^{2}h$. Then divide both sides by $\pi h$: $r^{2}=\frac{3V}{\pi h}$. Taking the square - root of both sides gives $r=\sqrt{\frac{3V}{\pi h}}$.

Step3: Substitute values

Substitute $V = 489.84$, $h = 13$, and $\pi\approx3.14$ into the formula: $r=\sqrt{\frac{3\times489.84}{3.14\times13}}$. First, calculate the numerator: $3\times489.84 = 1469.52$. Then calculate the denominator: $3.14\times13=40.82$. So, $r=\sqrt{\frac{1469.52}{40.82}}=\sqrt{36}$.

Step4: Calculate the value of $r$

$\sqrt{36}=6$.

Answer:

$6.00$