SOLUTION: How long a wire 0.1 inches in diameter can be drawn from a block of copper 2 by 4 by 6 in.?

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Question 918554: How long a wire 0.1 inches in diameter can be drawn from a block of copper 2 by 4 by 6 in.?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a wire 0.1in in diameter R
a wire is in shape of a cylinder, and we need to find a volume
V=r%5E2%2Api%2Ah where h is the length of a cylinder
since given diameter R=0.1in we can find radius using formula r=R%2F2
r=0.1in%2F2
r=0.05in , then we have
V=%280.05in%29%5E2%2A3.14%2Ah
V=0.0025in%5E2%2A3.14%2Ah
V=0.00785in%5E2%2Ah
since given dimensions of a block of copper and all will be used to make a wire, means that wire will have same volume as a block of copper;
so, find a volume of a block of copper:
2in by 4in by 6in
V=2in%2A4in%2A6in
V=48in%5E3
now plug it in V=0.00785in%5E2%2Ah
48in%5E3=0.00785in%5E2%2Ah.............solve for h
48in%5E3%2F0.00785in%5E2=h
48in%5Ecross%283%291%2F0.00785icross%28n%5E2%29=h
48in%2F0.00785=h
6114.65in=h ......the length of a wire