A cast iron pipe used as a water main for a home has an outer diameter of 11 in. If the pipe has a thickness of 0.25 in, what volume of iron does 30 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

To find the volume of iron in the 30 in of pipe, we need to first find the inner diameter of the pipe.

Inner diameter = Outer diameter - 2 * Thickness
Inner diameter = 11 in - 2 * 0.25 in
Inner diameter = 10.5 in

Next, we need to find the volume of the iron in 30 in of pipe.

Volume = π * (outer radius^2 - inner radius^2) * length

First, we need to find the outer and inner radii:
Outer radius = 11 in / 2 = 5.5 in
Inner radius = 10.5 in / 2 = 5.25 in

Now, we can calculate the volume:

Volume = π * (5.5^2 - 5.25^2) * 30
Volume ≈ 3.14159 * (30.25 - 27.5625) * 30
Volume ≈ 3.14159 * 2.6875 * 30
Volume ≈ 3.14159 * 80.625
Volume ≈ 253.335 cubic inches

Therefore, the volume of iron in 30 in of pipe is approximately 253.34 cubic inches.