SOLUTION: A rectangular piece of sheet metal with an area of 1,600 in2 is to be bent into a cylindrical length of stovepipe having a volume of 800 in3. What are the dimensions of the sheet m

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Question 812451: A rectangular piece of sheet metal with an area of 1,600 in2 is to be bent into a cylindrical length of stovepipe having a volume of 800 in3. What are the dimensions of the sheet metal?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The original 1600 in^2 piece has an x and a y length, each direction. ONE of them would become a circumference and the other will become a cylinder length or height.

Cylinder volume would be pi%2Ar%5E2%2Ah, but we would also have some relation between h and the original sheet area xy=1600. Let's use y as the cylinder height.
y=1600%2Fx, and if h=y, then
pi%2Ar%5E2%2Ay=pi%2Ar%5E2%2A%281600%2Fx%29=800

What can we learn about r and x ?
Circumference, 2%2Api%2Ar=x, because x is the other direction of the sheet, which becomes a circumference when the bending operation on the sheet is formed to make it into the cylinder. Solve this circumf equation for r and substitute into the 800 volume equation:

r=x%2F%282%2Api%29.
pi%2Ar%5E2%2A%281600%2Fx%29=800
pi%2A%28x%2F%282%2Api%29%29%5E2%2A%281600%2Fx%29=800
pi%28x%2Ax%2F%284%2Api%2Api%29%29%281600%2Fx%29=800
%28x%2A400%2Fpi%29=800
x=800%2Api%2F400
highlight%28x=2%2Api%29

and now with x known, back to xy=1600 lets you find y.