# SOLUTION: A rectangular piece of sheet metal with an area of 1200 in^2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in^3. What are the dimensions of the sheet

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 Question 66751This question is from textbook College Algebra : A rectangular piece of sheet metal with an area of 1200 in^2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in^3. What are the dimensions of the sheet metal? I am to come up with a system of equations to solve this problem. The sides of the rectangle are labeled x and y. I know that {x*y=1200 in^2}; x would be the circumference of the cylinder which would mean that {x=2(PI)r}; the volume would be {(PI)r^2(y)=600 in^3}. I just can't figure out how to show it all in terms of y and x to figure out the equation. Thanks. This question is from textbook College Algebra Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!You are correct in what you have done so far. Let's start with the volume of the cylindical pipe. Substitute r here with: from Simplify. Now substitute the y here with from the area, Simplify. Multiply both sides by Divide both sides by 1200. and, from above: The dimensions of the rectangular metal sheet are: by inches. or...using as an approximation: by or 6.28 by 191.08 inches.