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: Calculate outer radius

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

Step2: Calculate inner radius

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

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

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

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Step4: Calculate the value

\(V=27\times3.14159\times3.8475\approx27\times3.14159\times3.8475\approx328.19\)

Answer:

\(328.19\) cubic inches