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Question 1789: A rectangular piece of sheet metal with an area of 1200 in^2 is to be bent into a cylindrical length (right circular cylinder) of stovepipe having a volume of 600 in^3. What are the dimensions of the sheet metal?
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! these sorts of questions are lovely questions (yes, i guess i must be a sad individual)...anyway, draw a rectangle, vertical side a and horizontal side b
the area = ab = 1200
Now draw an upright cylinder (by wrapping the length b into a circle)...its radius is length r, and its height is a
Volume of this cyclinder is the area of the circular end times the height...
now, seeing as how i do not know what r is, i had better find it. This is found from the circumference of the circle (which is the length b)...
circumference, b = 
so, 
So, we can get rid of the r in the volume equation..this is now re-written as:
 . This can be simplified to
So we know the volume, but not a or b...2 unknowns in 1 equation is NOT good, so we need to get rid of either a or b...we do this by using the area equation, at the start of this explanation...let's re-write it as a = 1200/b
so we now get 
cancel the b with one of those in the  term, and simplifying the 1200 and 4 gives
so,  --> b=2pi
Substitute this into the area equation and you find a=600/pi. These are the dimensions of the sheet metal.
cheers
Jon.
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