SOLUTION: A piece of copper is described below: 4 in. in length. 2 in. wide. .5 in. thick. The piece is formed into a wire of uniform thickness and 100 yds. in length. Determ

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Question 1205156: A piece of copper is described below:
4 in. in length.
2 in. wide.
.5 in. thick.
The piece is formed into a wire of uniform thickness and 100 yds. in length.
Determine wire diameter.
Not sure how to solve.



Found 3 solutions by MathLover1, math_tutor2020, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A piece of copper is described below:
4in in length.
2in wide.
.5in thick.
the volume is:
V=4%2A2%2A.5in%5E3=4in%5E3...convert to cubic yards
V=8.573%2A10%5E-5%2Ayd%5E3

wire made of that piece of cupper is in shape of cylinder, l=100yd in length
V+=+pi+%2Ar%5E2+%2Al
8.573%2A10%5E-5%2A+yd%5E3=+pi%2Ar%5E2%2A100yd
8.573%2A10%5E-5+yd%5E2=+pi+%2Ar%5E2+%2A100
r%5E2=%288.573%2A10%5E-5%2Ayd%5E2%29%2F%28+pi%2A100%29
r%5E2=2.729%2A10%5E-7%2Ayd%5E2
r=sqrt%282.729%2A10%5E-7%2Ayd%5E2%29
r=0.000522398yd....convert to inches
r=0.0188in
.
then, wire diameter is:
d=2%2Ar
d=0.0376in


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1 yard = 3 feet
1 foot = 1/3 of a yard
12 inches = 1/3 of a yard
1 inch = (1/12)*(1/3) of a yard
1 inch = 1/36 of a yard

Or you could say
1 ft = 12 inches
3 ft = 36 inches = 1 yard
36 inches = 1 yard
1 inch = 1/36 of a yard

Use that last equation to find that
4 inches = 4/36 = 1/9 of a yard
2 inches = 2/36 = 1/18 of a yard
0.5 inches = 0.5/36 = 1/72 of a yard

Then,
volume = (1/9)*(1/18)*(1/72)
volume = 0.00008573 cubic yards

The wire formed is a cylinder of length 100 yards and radius r.
volume of cylinder = pi*(radius)^2*(height)
V = pi*r^2*h
V = pi*r^2*100
V = 100pi*r^2
100pi*r^2 = 0.00008573
r^2 = 0.00008573/(100pi)
r^2 = 0.000 000 272 887
r = sqrt(0.000 000 272 887)
r = 0.0005223858727033
d = diameter
d = 2*r
d = 2*0.0005223858727033
d = 0.001044771745407
This measure is in yards.

Multiply by 36 to convert from yards to inches.
You should get roughly 0.03761178 inches.

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Another approach:

volume of initial slab = 4*2*0.5 = 4 cubic inches.

1 yard = 36 inches, which means we multiply by 36 to convert from yards to inches.
100 yards = 100*36 = 3600 inches.

Volume of a cylinder = pi*(radius)^2*(height)
V = pi*r^2*h
V = pi*r^2*3600
V = 3600pi*r^2

3600pi*r^2 = 4
r^2 = 4/(3600pi)
r^2 = 0.0003 5368
r = sqrt(0.0003 5368)
r = 0.01880638
d = 2*r
d = 2*0.01880638
d = 0.03761276
We get roughly the same diameter as before. There's a bit of rounding error but the 0.03761 part is the same.

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Answer:

Wire diameter = 0.03761 inches (approximate)
Round this value however needed.
It makes more sense to report the answer in inches rather than yards. But feel free to use yards instead if your teacher requires it.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

We are making the volume of a rectangular solid into a long thin cylinder.
The length of the wire (the "height", h, of the cylinder) is 100 yards, a 
yard is 36 inches so h = 3600 inches.

L%2AW%2AH%22%22=%22%22pi%2Ar%5E2%2Ah

4%2A2%2A0.5%22%22=%22%22pi%2Ar%5E2%2A3600

%284%2A2%2A0.5%29%2F%28pi%2A3600%29%22%22=%22%22r%5E2

sqrt%28%284%2A2%2A0.5%29%2F%28pi%2A3600%29%29%22%22=%22%22r

0.0188063195%22%22=%22%22r

diameter = 2r = 2(0.188063195) = 0.0376126389 inches.

Round off as you were told.

Edwin