SOLUTION: An iron pipe 10 ft. long has an internal diameter of 1 ft. If the iron is 1/2 in. thick, find the volume of metal in the pipe.

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Question 957805: An iron pipe 10 ft. long has an internal diameter of 1 ft. If the iron is 1/2 in. thick, find the volume of metal in the pipe.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since the metal of the pipe forms a tube and since it is unlikely you have a formula for the volume of a tube, we must find the volume of the tube by adding or subtracting volumes we can find.
The pipe, with the air inside of it, forms a cylinder. Just the air inside the pipe also forms a cylinder. And there is a well-known formula for the volume of a cylinder:
V+=+pi%2Ar%5E2%2Ah
The volume of the metal in the pipe, the tube, will be the volume of the pipe and the air minus the volume of the air.

Now we just need to find the values for the volume formula: the radius and hieght of each cylinder. The internal diameter of the pipe is 1 foot. This makes the radius of the air 1/2 feet. The thickness of the pipe is 1/2 inch or 1/24 foot. This makes the radius of the pipe-and-air cylinder:
1%2F2+%2B+1%2F24+=+12%2F24+%2B+1%2F24+=+13%2F24 feet. The height of both cylinders is 10 feet.

Now we can indert these values into our volume formula. For the pipe-and-air cylinder:
V+=+pi%2A%2813%2F24%29%5E2%2A10+=+pi%2A%28169%2F576%29%2A10+=+%28845%2F288%29pi cu. ft.

For the air-only cylinder:
V+=+pi%2A%281%2F2%29%5E2%2A10+=+pi%2A%281%2F4%29%2A10+=+%285%2F2%29pi cu. ft.

For the volume of the metal of the pipe we subtract these:
V+=+%28845%2F288%29pi+-+%285%2F2%29pi cu. ft.
V+=+%28845%2F288%29pi+-+%28720%2F288%29pi cu. ft.
V+=+%28125%2F288%29pi cu. ft.
This is an exact expression for the volume of the metal of the pipe.