Question

the volume of a cylinder is given by the formula $v = \pi r^{2}h$ where $r$ is the radius of the base and $h$ is the height of the cylinder. a cylindrical vat holds 5,600 cubic meters of liquid when filled to a height of 25 meters. what is the radius of the vat? use $\pi = 3.14$. round your answer to the nearest tenth. the radius of the vat is meters.

Explanation:

Step1: Rearrange the volume formula for \(r\)

Given \(V=\pi r^{2}h\), we can solve for \(r^{2}\) first: \(r^{2}=\frac{V}{\pi h}\).

Step2: Substitute the given values

We know \(V = 5600\) cubic meters, \(h=25\) meters, and \(\pi = 3.14\). Substituting these into the formula for \(r^{2}\):
\(r^{2}=\frac{5600}{3.14\times25}\)

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Step3: Solve for \(r\)

Take the square - root of \(r^{2}\): \(r=\sqrt{r^{2}}\), so \(r=\sqrt{71.34}\approx8.4\)

Answer:

\(8.4\)