Question

the volume of this cylinder is 157,075.36 cubic meters. what is the radius? round your answer to the nearest hundredth. 74 m r ≈ meters

Explanation:

Step1: Write the formula for the volume 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. Given \(V = 157075.36\) cubic meters and \(h=74\) meters, and taking \(\pi\approx3.14\).

Step2: Rearrange the formula to solve for \(r^{2}\)

From \(V=\pi r^{2}h\), we can get \(r^{2}=\frac{V}{\pi h}\). Substitute the values: \(r^{2}=\frac{157075.36}{3.14\times74}\).
First, calculate \(3.14\times74 = 232.36\). Then \(r^{2}=\frac{157075.36}{232.36}=676\).

Step3: Solve for \(r\)

Since \(r^{2}=676\), then \(r=\sqrt{676}\). \(r = 26.00\) (because \(26\times26 = 676\))

Answer:

\(26.00\) meters