SOLUTION: 1. A local farm owner has just acquired another smaller farm with three silos for cattle feed. The shapes of the silos are right circular cylinders. Suppose one silo is 40 ft tall
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Question 758137: 1. A local farm owner has just acquired another smaller farm with three silos for cattle feed. The shapes of the silos are right circular cylinders. Suppose one silo is 40 ft tall with a twelve foot diameter; another silo is 50ft tall with a 14ft diameter; and the third silo is 60ft tall with an 18ft diameter.
a. What is the combined capacity in cubic feet of al three silos?
b. If 1 quart of paint covers 100 sq feet, how many quarts of paint will the farmer need to paint the three silos and restore an appearance of newness?
You can put this solution on YOUR website! Volume of a right circular cylinder
= Pi r^2 h
Ist Silo = Pi *6^2 * 40 = 4523.89 cuft
2nd Silo = Pi * 7^2 * 50 = 7696.90 cuft
3rd Silo = Pi * 9^2 * 60 = 15268.14 cuft
Total Volume = 27488.93 cuft.
Surface Area of a right circular cylinder
= Pi r^2 + 2 Pi r h (Assuming only the top
of the silo needs painting.)
1st Silo= Pi * 6^2 + 2*Pi*6*40 = 1621.06 ft^2
2nd Silo = Pi * 7^2 + 2+Pi*7*50 = 2353.05 ft^2
3rd Silo = Pi * 9^2 + 2 * Pi * 9 * 60 = 3647.39 ft^2
Total Surface Area = 7621.5 ft^2
Divided by 100 sq ft = 76 215
Requiring 77 quarts of paint.
