7. thirty-two babbitt bearing liners must be poured as shown. each babbitt ingot is 4 cubic inches in…

Explanation:

Step1: Identify the shape and dimensions

The liner is a hollow semi-cylinder with inner radius $r = 1\frac{1}{8}''$, thickness $t = \frac{3}{16}''$, and length $L = 4\frac{1}{8}''$.

Step2: Calculate the outer radius

$$R = r + t = 1\frac{1}{8} + \frac{3}{16} = \frac{9}{8} + \frac{3}{16} = \frac{18}{16} + \frac{3}{16} = \frac{21}{16} \text{ in}$$

Step3: Calculate the cross-sectional area

$$A = \frac{1}{2} \pi (R^2 - r^2) = \frac{1}{2} \pi \left( \left(\frac{21}{16}\right)^2 - \left(\frac{18}{16}\right)^2 \right) = \frac{1}{2} \pi \left( \frac{441 - 324}{256} \right) = \frac{117\pi}{512} \text{ sq in}$$

Step4: Calculate volume of one liner

$$V_{one} = A \times L = \frac{117\pi}{512} \times \frac{33}{8} = \frac{3861\pi}{4096} \approx 2.961 \text{ cubic inches}$$

Step5: Calculate total volume for 32 liners

$$V_{total} = 32 \times V_{one} = 32 \times \frac{3861\pi}{4096} = \frac{3861\pi}{128} \approx 94.75 \text{ cubic inches}$$

Step6: Calculate the number of ingots

$$\text{Ingots} = \frac{V_{total}}{V_{ingot}} = \frac{94.75}{4} \approx 23.69$$

Step7: Round to the nearest whole ingot

Since partial ingots cannot be used for a full pour, round up. $$\text{Ingots} \approx 24$$

Answer:

24 Babbitt ingots