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 26 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

Check the picture below.

`\textit{Area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\textit{outer radius}\\ r=\textit{inner radius}\\[-0.5em] \hrulefill\\ R=4.5\\ r=4.05 \end{cases}\implies \begin{array}{llll} A=\pi (4.5^2-4.05^2) \\\\\\ A=3.8475\pi ~in^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE volume of the pipe}}{(27)(A)\implies (27~in)(3.8475\pi ~in^2) ~~ \approx ~~ \text{\LARGE 326.36}~in^3}`