Question
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.)
Answers
GPT 3.5
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.
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.
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