Question

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

Explanation:

Step1: Identify the shape of the solid

When the rectangle is rotated about side \(PS\), a cylinder is formed. The radius \(r\) of the cylinder is equal to the length of \(PQ = 6\), and the height \(h\) of the cylinder is equal to the length of \(QR=11\).

Step2: Use the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 6\) and \(h = 11\) into the formula:

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Step3: Calculate the numerical value

Using \(\pi\approx3.14\), we have \(V = 396\times3.14=1243.44\)

Answer:

\(1243.4\)