Question

question
find the volume of the solid generated when the rectangle below is rotated about side (overline{eh}).
round your answer to the nearest tenth if necessary.
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Explanation:

Step1: Recall the formula for the volume of a cylinder

When a rectangle is rotated about one of its sides, it forms a cylinder. The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Here, if we rotate the rectangle about side \(EH\), the radius \(r = EF=7\) and the height \(h=HG = 6\).

Step2: Substitute the values into the formula

Substitute \(r = 7\) and \(h=6\) into the formula \(V=\pi r^{2}h\). We get \(V=\pi\times7^{2}\times6\).
First, calculate \(7^{2}=49\). Then \(V=\pi\times49\times6=294\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14\), we have \(V = 294\times3.14=923.16\).

Answer:

\(923.2\)