Question

a cast iron pipe used as a water main for a home has an outer diameter of 9 in. if the pipe has a thickness of 0.45 in, what volume of iron does 27 in of pipe contain? answer in cubic inches. round your answer to the nearest hundredth if necessary. (note: diagram is not drawn to scale.)

Explanation:

Step1: Find the outer radius

The outer diameter is \(d = 9\) inches, so the outer radius \(R=\frac{d}{2}=\frac{9}{2}=4.5\) inches.

Step2: Find the inner radius

The thickness is \(0.45\) inches. So the inner radius \(r=R - 0.45=4.5 - 0.45 = 4.05\) inches.

Step3: Use the formula for the volume of a hollow cylinder

The formula for the volume of a hollow cylinder is \(V=\pi h(R^{2}-r^{2})\), where \(h = 27\) inches.
Substitute \(R = 4.5\), \(r = 4.05\), and \(h=27\) into the formula:

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Step4: Calculate the value

\(V=27\times3.14\times3.8475\)
\(V = 84.78\times3.8475\)
\(V\approx328.00\)

Answer:

\(328.00\) cubic inches