Question

A cast iron pipe used as a water main for a home has an outer diameter of 13 in. If the pipe has a thickness of 0.45 in, what volume of iron does 21 in of pipe contain? Answer in cubic inches. Round your answer to the nearest hundredth if necessary. (Note: diagram is not drawn to scale

Answer 1

We need to find the volume of iron that 21 in of pipe contains.

In order to do so, we need to subtract the volume of the inner cylinder from the volume of the outer cylinder.

The volume V of a cylinder of radius r and height h is:

$V=\pi r^2h$

For this problem, we have:

$\begin{gathered} h=21\text{ in} \\ \\ r_{outer}=\frac{13}{2}\text{ in }=6.5\text{ in} \\ \\ r_{inner}=6.5-0.45\text{ in }=6.05\text{ in} \end{gathered}$

Thus, we obtain:

$\begin{gathered} V_{outer}-V_{inner}=\pi(r_{outer}^2-r_{inner}^2)h \\ \\ =\pi(6.5^2-6.05^2)\cdot21\text{ in}^3 \\ \\ \cong372.59\text{ in}^3 \end{gathered}$

Answer: 372.59 in³