Problem

For the steel pipe shown, the wall thickness is 1/4 inch and the outer diameter is 2 inches. If the pipe is 1 foot long, what volume of steel is it made of?

Answer

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Answer

Final Answer: The volume of the steel the pipe is made of is approximately 16.49 cubic inches.

Steps

Step 1 :Given that the outer diameter of the steel pipe is 2 inches, the wall thickness is 14 inch, and the length of the pipe is 1 foot (or 12 inches).

Step 2 :The outer radius of the pipe is half of the outer diameter, which is 1 inch. The inner radius of the pipe is the outer radius minus the wall thickness, which is 114=34 inch.

Step 3 :The volume of a cylinder is given by the formula πr2h, where r is the radius and h is the height (or length in this case).

Step 4 :Calculate the volume of the outer cylinder using the formula πr2h, where r is the outer radius (1 inch) and h is the length of the pipe (12 inches). This gives a volume of approximately 37.699 cubic inches.

Step 5 :Calculate the volume of the inner cylinder using the formula πr2h, where r is the inner radius (34 inch) and h is the length of the pipe (12 inches). This gives a volume of approximately 21.206 cubic inches.

Step 6 :The volume of the steel the pipe is made of is the difference between the volume of the outer cylinder and the volume of the inner cylinder. This is approximately 37.69921.206=16.493 cubic inches.

Step 7 :Final Answer: The volume of the steel the pipe is made of is approximately 16.49 cubic inches.

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