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) (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 , but we would also have some relation between h and the original sheet area . Let's use y as the cylinder height.
, and if h=y, then
What can we learn about r and x ?
Circumference, , 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:
.
and now with x known, back to xy=1600 lets you find y.
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