Problema Solution
An open cylindrical tank is 150 feet in diameter and 180 feet high. The lateral surface area of the tank (no top and no bottom) is to be painted with paint that covers square feet per gallon. When filled each cubic foot of the tank holds approximately 7.5 gallons of gasoline valued at $2.75 per gallon. Find the number of gallons of paint required for a single coat of paint. Find the total value of the gasoline in the filled tank.
Answer provided by our tutors
The surface of the area that needs to be painted is:
A = 2*(150/2)*pi*180 (pi = 3.14)
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A = 64,823 ft^2
Since 1 gallon covers 1 ft^2 we will need 64,823 gallons of paint.
Next we find the volume of the cylinder:
V = (150/2)^2 *pi*180
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V = 3,180,862.56 ft^3
1 ft^3 holds 7.5 gal of gasoline this means that 3,180,862.56 ft^3 will hold 3,180,862.56*7.5 gal of gasoline.
The cost per gallon is $2.75 so the total value of the gasoline in the filled tank is:
3,180,862.56*7.5*2.75 = $65,605,290.30