Question 95073: A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is $4.00, while the cylindrical part costs $2.00 per square foot. If the tank needs to hold 10(pi symbol)ft^3 of propane gas, what dimensions minimize the cost of construction? What is the minimum cost?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is $4.00, while the cylindrical part costs $2.00 per square foot. If the tank needs to hold 10(pi symbol)ft^3 of propane gas, what dimensions minimize the cost of construction? What is the minimum cost?
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Let the radius be "x" feet.
Area of the combined semi-circular end pieces = 4pir^2 = 4(pi)x^2
Volume of the combined semi-circular end pieces = (4/3)(pi)x^3
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Area of the cylindrical part = 2(pi)xh
Volume of the cylindrical part = (pi)x^2h
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EQUATION:
volumn + volumn = volumn
(4/3)(pi)x^3 + (pi)x^2h = 10(pi)
(4/3)x^3 + x^2h - 10 = 0
Comment: Not knowing "h" results in not knowing "x".
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Price equation:
price + price = total price
4[4(pi)x^2] + 2[2(pi)xh] = total price
Comment: Not knowing "h" results in not being able to find the minimum here.
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Cheers,
Stan H.
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