Question

the volume of this cone is 1,394.03754 cubic meters. what is the radius of this cone? round your answer to the nearest hundredth. 20.3 m r ≈ meters

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$. We know $V = 1394.03754$ m³ and $h=20.3$ m.

Step2: Rearrange formula for radius

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can solve for $r^{2}$ first: $r^{2}=\frac{3V}{\pi h}$. Then $r = \sqrt{\frac{3V}{\pi h}}$.

Step3: Substitute values

Substitute $V = 1394.03754$, $h = 20.3$ and $\pi\approx3.14$ into the formula: $r=\sqrt{\frac{3\times1394.03754}{3.14\times20.3}}$.
First, calculate the value inside the square - root: $\frac{3\times1394.03754}{3.14\times20.3}=\frac{4182.11262}{63.742}\approx65.61$.
Then, find $r$: $r=\sqrt{65.61}\approx 8.10$.

Answer:

$8.10$