A 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? What are the dimensions of sheet metal, Pre-calc question using matrix?
It will be assumed that the original sheet of metal is rectangular in shape. Hence
Area of sheet metal = A = LW
where
L = length of the sheet metal
W = width of the sheet metal
Therefore,
LW = 1200 --- call this Equation 1
If the sheet metal will be rolled along its length then its volume will be
V = volume = (蟺/4)L^2W --- Equation 2
where
L = diameter of the stove pipe
W = height of the stove pipe
From Equation 1, W = 1200/L and substituting this into Equation 2,
V = 600 = (蟺/4)(L^2)(1200/L)
Simplifying,
600 = (蟺/4)(1200L)
L = 2/蟺 and solving for W (using Equation 1),
W = 1200/(2/蟺)
W = 600蟺 in.
ANSWER
Diameter = 2/蟺
Height = 600蟺
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