SOLUTION: A rectangular piece of sheet metal with an area of 1200 in2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in3. What are the dimensions of the sheet me

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Question 1201847: A rectangular piece of sheet metal with an area of 1200 in2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in3. What are the dimensions of the sheet metal? (Round your answer to one decimal place.)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the width of the piece of sheet metal, and let y be its length.

Roll the sheet lengthwise to form the cylinder; the height of the cylinder is x and the circumference of the cylinder is y. Then the radius of the cylinder is circumference divided by 2pi, or y/(2pi).

Then

[1] xy+=+1200 [the area of the piece of sheet metal is 1200 sq in]
[2] %28pi%29x%28y%5E2%2F%284pi%5E2%29%29=600 [the volume of the cylinder (%28pi%29%28r%5E2%29h) is 600 cu in]

Substitute [1] in [2]:

%28pi%29%28xy%29%28y%29%2F%284pi%5E2%29=600
%28pi%291200%28y%29%2F%284pi%5E2%29=600
2y%2F%284pi%29=1
2y=4pi
y=2pi

Substitute that in [1] to find x:

x%282pi%29=1200
x=600%2Fpi

ANSWERS:
width: x=600%2Fpi
length: y=2pi

You can evaluate those dimensions and do the rounding....