Question

the volume of this cone is 25,835.92 cubic centimeters. what is the radius of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 51 cm r ≈ centimeters

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. We know $V = 25835.92$ cm³, $h=51$ cm and $\pi\approx3.14$.

Step2: Rearrange formula for radius

First, substitute the known values into the formula: $25835.92=\frac{1}{3}\times3.14\times r^{2}\times51$.
Then simplify the right - hand side: $\frac{1}{3}\times3.14\times51 = 53.38$. So the equation becomes $25835.92 = 53.38r^{2}$.
Next, solve for $r^{2}$: $r^{2}=\frac{25835.92}{53.38}=484$.
Finally, solve for $r$: $r=\sqrt{484}=22.00$ cm.

Answer:

$22.00$