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…

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 0.4 in, what volume of iron does 22 in of pipe contain? answer in cubic inches. round your answer to the nearest hundredth if necessary. (note: diagram is not drawn to scale.)

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 0.4 in, what volume of iron does 22 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

Explanation:

Step1: Find outer radius

Outer diameter is 13 in, so outer radius $r_1=\frac{13}{2}=6.5$ in.

Step2: Find inner radius

Pipe thickness is 0.4 in, so inner radius $r_2 = 6.5 - 0.4=6.1$ in.

Step3: Use volume formula for hollow - cylinder

Volume of a hollow - cylinder $V=\pi h(r_1^{2}-r_2^{2})$, where $h = 22$ in. $V=\pi\times22\times(6.5^{2}-6.1^{2})$

Step4: Calculate the values inside the parentheses

$6.5^{2}=42.25$ and $6.1^{2}=37.21$. Then $6.5^{2}-6.1^{2}=42.25 - 37.21 = 5.04$.

Step5: Calculate the volume

$V=\pi\times22\times5.04\approx3.14\times22\times5.04 = 348.4608\approx348.46$ in³.

Answer:

348.46 in³