SOLUTION: A length of pipe is to be made from 100 lbs. of lead. Determine length of pipe. Description of pipe: Diameter: 3/4 in. Thickness: 1/8 in. Lead weighs 2/3 lbs. per cu.

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Question 1046258: A length of pipe is to be made from 100 lbs. of lead. Determine length of pipe.
Description of pipe:
Diameter: 3/4 in.
Thickness: 1/8 in.
Lead weighs 2/3 lbs. per cu. in.
Let l = length.
Unsure how to proceed.

Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.
A length of pipe is to be made from 100 lbs. of lead. Determine length of pipe.
Description of pipe:
Diameter: 3/4 in.
Thickness: 1/8 in.
Lead weighs 2/3 lbs. per cu. in.
Let l = length.
Unsure how to proceed.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1.  From one side, the volume of lead is  V = 100%2F%28%282%2F3%29%29 = 300%2F2 = 150 cubic inches.


2.  From the other side, the volume of the solid body which is formed by the wall of the pipe, is 

    V = pi%2A%28D%2F2%29%5E2%2AL - pi%2A%28d%2F2%29%5E2%2AL,  

      where D = 3%2F4 in is the outer diameter,  d = 3%2F4+-+2%2A%281%2F8%29 = 3%2F4+-+1%2F4 = 2%2F4 = 1%2F2 in is the inner diameter.

    So,  V = %28%28pi%2AL%29%2F4%29%2A%28%283%2F4%29%5E2-%282%2F4%29%5E2%29 

           = %28%28pi%2AL%29%2F4%29%2A%289%2F16-4%2F16%29 = %28%28pi%2AL%29%2F4%29%2A%285%2F16%29 = pi%2AL%2A%285%2F64%29.


3.  Therefore, you have an equation

    pi%2AL%2A%285%2F64%29 = 150.


    Solve it for L, the tube length:

    L = %28150%2A64%29%2F%28pi%2A5%29 = %2830%2A64%29%2Fpi = 611.46 inches.

Answer.  611.46 inches.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
My method would be to consider the pipe to be a solid
cylinder of length +L+ and then subtract away the volume
of the hollow inside cylinder, giving you the pipe.
------------------------------
Area of the outside circle is:
+pi%2A%28%281%2F2%29%2A%283%2F4%29%29%5E2+
+pi%2A%283%2F8%29%5E2+
+%28+9%2F64+%29%2Api+
------------------------------
Area of the inside circle is:
+pi%2A%28%281%2F2%29%2A%285%2F8%29%29%5E2+
+pi%2A%28+5%2F16+%29%5E2+
+%28+25%2F256+%29%2Api+
----------------------
The cross section area of actual pipe is:
+%28+9%2F64+-+25%2F256+%29%2Api+
+%28+36%2F256+-+25%2F256+%29%2Api+
+%28+11%2F256+%29%2Api+
This area times +L+ is the volume of the pipe in in3
----------------------
Density in lbs/in3 times volume in in3 = weight of lead in pounds
+%282%2F3%29%2A%28+11%2F256+%29%2Api%2AL+=+100+
+L+=+100%2A%28+3%2F2%29%2A%28+256%2F11+%29%2A%281%2Fpi+%29+
+L+=+300%2A%28+128%2F11+%29%2A%28+1%2Fpi+%29+
+L+=+300%2A11.6364%2A.31831+
+L+=+300%2A3.70397+
+L+=+1111.1913+
The pipe is 1111.1913 inches long
or
+1111.1913%2F12+=+92.5993+
92.5993 ft long
-------------------
check my math. The method makes sense to me, but
my math could be WAY off!