Question

1. a length of brass pipe is shown in figure 28 - 35.

figure 28 - 35
details
the pipe measures 30 feet 0 inches long. the inside diameter is 1.50 inches and the outside diameter is 1.90 inches.
a. find the number of cubic inches of brass contained in the pipe.
b. brass weighs 526 pounds per cubic foot. what is the weight of the pipe?

Explanation:

Step1: Convert length to inches

Since \(1\) foot \( = 12\) inches, the length \(L\) of the pipe is \(L=30\times12 = 360\) inches.

Step2: Calculate radii

The outside radius \(R=\frac{1.90}{2}=0.95\) inches. The inside radius \(r = \frac{1.50}{2}=0.75\) inches.

Step3: Use the formula for the volume of a hollow cylinder

The volume \(V\) of a hollow - cylinder is \(V=\pi h(R^{2}-r^{2})\). Substitute \(h = L=360\), \(R = 0.95\), and \(r = 0.75\) into the formula:

$$
LATEXBLOCK0
$$

Step4: Convert volume from cubic inches to cubic feet for part (b)

Since \(1\) cubic foot \(=12\times12\times12 = 1728\) cubic inches. Let \(V_f\) be the volume in cubic feet. Then \(V_f=\frac{384.336}{1728}\approx0.2224\) cubic feet.

Step5: Calculate the weight of the pipe

If brass weighs \(526\) pounds per cubic foot, then the weight \(W\) of the pipe is \(W = 526\times V_f\). Substitute \(V_f\approx0.2224\) into the formula: \(W=526\times0.2224\approx117.0\) pounds

Answer:

a. The volume of brass in the pipe is approximately \(384.34\) cubic inches.
b. The weight of the pipe is approximately \(117.0\) pounds.