SOLUTION: A hollow cylindrical pipe is made of copper. The volume of the metal used in the pipe is 748cu.cm. Its external radius is 9 cm and length is 14 cm. Find the thickness of the pipe.

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Question 185572: A hollow cylindrical pipe is made of copper. The volume of the metal used in the pipe is 748cu.cm. Its external radius is 9 cm and length is 14 cm. Find the thickness of the pipe.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One approach to this problem is to imagine that the copper pipe is split down its length and laid open to give you a rectangular prism whose height is the same as the length of the pipe (14cm) and whose length is the same as the outside circumference of the copper pipe (2%2Api%2Ar) and the width is the thickness of the copper pipe which can be expressed in terms of the difference of the external radius and the internal radius (R%5Bo%5D-r%5Bi%5D).
The volume of such a prism is given by:
V+=+L%2AW%2Ah where: L+=+2%2Api%2AR%5Bo%5D, W+=+R%5Bo%5D-r%5Bi%5D, and h = 14cm.
Substituting V = 748, we get:
748+=+%282%2Api%2A9%29%2A%28R%5Bo%5D-r%5Bi%5D%29%2814%29 Simplifying this:
748+=+252%2Api%2A%28R%5Bo%5D-r%5Bi%5D%29 Divide both sides by 252%2Api
0.945+=+R%5Bo%5D-r%5Bi%5D
The thickness of the copper pipe is 0.945cm