Question 1046258
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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.
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1.  From one side, the volume of lead is  V = {{{100/((2/3))}}} = {{{300/2}}} = 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*(D/2)^2*L}}} - {{{pi*(d/2)^2*L}}},  

      where D = {{{3/4}}} in is the outer diameter,  d = {{{3/4 - 2*(1/8)}}} = {{{3/4 - 1/4}}} = {{{2/4}}} = {{{1/2}}} in is the inner diameter.

    So,  V = {{{((pi*L)/4)*((3/4)^2-(2/4)^2)}}} 

           = {{{((pi*L)/4)*(9/16-4/16)}}} = {{{((pi*L)/4)*(5/16)}}} = {{{pi*L*(5/64)}}}.


3.  Therefore, you have an equation

    {{{pi*L*(5/64)}}} = 150.


    Solve it for L, the tube length:

    L = {{{(150*64)/(pi*5)}}} = {{{(30*64)/pi}}} = 611.46 inches.

<U>Answer</U>.  611.46 inches.
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