Question

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the volume of this cylinder is 251.2 cubic centimeters. what is the radius?
round your answer to the nearest hundredth.
5 cm
r = centimeters
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Explanation:

Step1: Recall the volume formula of a cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(V = 251.2\) cubic centimeters and \(h=5\) centimeters, and taking \(\pi = 3.14\).
We have \(251.2=3.14\times r^{2}\times5\).
First, simplify the right - hand side: \(3.14\times5 = 15.7\). So the equation becomes \(251.2 = 15.7r^{2}\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(251.2 = 15.7r^{2}\) by \(15.7\):
\(r^{2}=\frac{251.2}{15.7}\).
\(r^{2}=16\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r = \sqrt{16}\) or use the formula \(r=\sqrt{\frac{V}{\pi h}}\).
Another way: from \(r^{2}=16\), \(r = 4.00\) (exact value in this case, but if we use the formula \(r=\sqrt{\frac{V}{\pi h}}\) with \(\pi = 3.14\), \(V = 251.2\), \(h = 5\))
\(r=\sqrt{\frac{251.2}{3.14\times5}}=\sqrt{\frac{251.2}{15.7}}=\sqrt{16}=4.00\)

Answer:

\(4.00\) centimeters