Question

the volume of this cylinder is 12,560 cubic meters. what is the radius? round your answer to the nearest hundredth.

Explanation:

Step1: Recall volume formula

The volume formula for a cylinder is $V = \pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We know $V = 12560$ cubic - meters and $h = 10$ meters.

Step2: Substitute values into formula

Substitute $V = 12560$ and $h = 10$ into $V=\pi r^{2}h$, we get $12560=\pi r^{2}\times10$.

Step3: Solve for $r^{2}$

First, divide both sides of the equation $12560 = 10\pi r^{2}$ by $10\pi$. So $r^{2}=\frac{12560}{10\pi}=\frac{1256}{\pi}$.

Step4: Calculate $r$

Take the square - root of both sides. $r=\sqrt{\frac{1256}{\pi}}$. Using $\pi\approx3.14$, we have $r=\sqrt{\frac{1256}{3.14}}=\sqrt{400}= 20.00$.

Answer:

$20.00$