Question

in the figure, a hollow steel pipe is in the shaped of a right - circular cylinder. the steel pipe has an outside diameter of 48 inches, a wall thickness of 5 inches, and a height of 144 inches. which of the following is closest to the volume, in cubic inches, of the wall of this steel pipe? a. 177 b. 505 c. 2,100 d. 13,395 note: figure not drawn to scale.

Explanation:

Step1: Calculate outer - radius

The outer diameter $d_{out}=48$ inches, so the outer - radius $r_{out}=\frac{d_{out}}{2}=\frac{48}{2} = 24$ inches.

Step2: Calculate inner - radius

The wall thickness $t = 0.5$ inches. So the inner - radius $r_{in}=r_{out}-t=24 - 0.5=23.5$ inches.

Step3: Use the volume formula for a hollow cylinder

The volume formula for a hollow cylinder is $V=\pi h(r_{out}^{2}-r_{in}^{2})$, where $h = 144$ inches.
Substitute the values:
\[

$$\begin{align*} V&=\pi\times144\times(24^{2}-23.5^{2})\\ &=144\pi\times(24 + 23.5)\times(24 - 23.5)\\ &=144\pi\times47.5\times0.5\\ &=144\pi\times23.75\\ &=144\times3.14\times23.75\\ &=452.16\times23.75\\ & = 10748.7 \end{align*}$$

\]

Step4: Compare with options

The value closest to $10748.7$ is $10505$ (option b).

Answer:

b. 505