Question

question
a cast iron pipe used as a water main for a home has an outer diameter of 11
in. if the pipe has a thickness of 0.35 in, what volume of iron does 23 in of
pipe contain? answer in cubic inches. round your answer to the nearest
hundredth if necessary. (note: diagram is not drawn to scale.)
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Explanation:

Step1: Find the outer radius

The outer diameter is \(d = 11\) inches. The outer radius \(R=\frac{d}{2}=\frac{11}{2}=5.5\) inches.

Step2: Find the inner radius

The thickness of the pipe is \(0.35\) inches. The inner radius \(r=R - 0.35=5.5 - 0.35 = 5.15\) inches.

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

The formula for the volume of a hollow - cylinder (the volume of the iron in the pipe) is \(V=\pi h(R^{2}-r^{2})\), where \(h = 23\) inches.
Substitute \(R = 5.5\), \(r = 5.15\), and \(h = 23\) into the formula:

$$
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$$

Step4: Calculate the value

$$
LATEXBLOCK1
$$

Answer:

\(269.33\) cubic inches