SOLUTION: How many feet of piping can be made from 5 cubic feet of iron if the outer and inner diameters of the pipe are 8 and 6 inches, respectively?

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Question 1197026: How many feet of piping can be made from 5 cubic feet of iron if the outer and inner diameters of the pipe are 8 and 6 inches, respectively?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Those diameters are 2%2F3 feet for outer, and 1%2F2 feet for inner.
As RADII, 1%2F3 feet for outer, and 1%2F4 feet for inner.

Cross section area of the piping:
* cross%28pi%281%2F3-1%2F4%29%5E2%29 SQUARE feet ------------ this line wrong. See below.


How long L for 5 cubic feet?
cross%28L%2Api%2A%281%2F3-1%2F4%29%5E2=5%29--------simplify and solve for L.


*
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Cross section area of piping:
pi%2A%281%2F3%29%5E2-pi%2A%281%2F4%29%5E2
pi%2A%281%2F9-1%2F16%29
pi%2A%28%2816-9%29%2F%289%2A16%29%29
pi%2A%287%2F16%29

The volume to be 5 cubic feet, length L
L%2Api%2A%287%2F16%29=5---------simplify and solve for L.

Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
How many feet of piping can be made from 5 cubic feet of iron
if the outer and inner diameters of the pipe are 8 and 6 inches, respectively?
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            The solution by @josgarithmetic is  INCORRECT,  as usual.

            I came to bring a correct solution. 


Outer diameter is 8 inches = 2%2F3 ft;  inner diameter is 6 inches = 1%2F2 ft.

Outer radius is  1%2F3 ft;  inner radius is  1%2F4 ft.


The cross-section area is  A = pi%2A%281%2F3%29%5E2 - pi%2A%281%2F4%29%5E2 = pi%2A%281%2F9-1%2F16%29 = pi%2A%28%2816-9%29%2F%289%2A16%29%29 = pi%2A%287%2F144%29 square feet.


For the pipe length L we have this equation

    A*L = 5 cubic feet,  or  pi%2A%287%2F144%29%2AL = 5.


From this equation

    L = 5%2F%28pi%2A%287%2F144%29%29 = %285%2A144%29%2F%283.14159%2A7%29 = 32.74 ft  (rounded).   


ANSWER.  The pipe length is about 32.74 ft.

Solved.

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Formula in the post by @josgarithmetic is  INCORRECT - - - even do not try to use it.

For your safety,  you better ignore his post.


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He re-wrote everything from me after seeing my post.