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Question 1088949: A tank is a vertical cylinder with inside diameter of 6ft and a height of 15ft.
a. What is the volume of liquid in cubic feet if we fill the tank to one foot high?
b. What is the total volume of the tank in cubic feet?
c. What is the volume of water in cubic ft in the tank if a measure stick indicates the water surface is 6 feet below the top of the tank?
d. What is the weight in pounds of the tank, as in the above case, if the tank itself weighs 20 lbs per ft of height?
e. How much water in gallons would have to be removed to reduce the total weight of the tank plus water, as in the above case, by 20%?
f. What would be the new level of the water, as measured from the top of the tank, if the water in the above case (equivalent of 20% of total weight) is removed?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A tank is a vertical cylinder with inside diameter of 6ft and a height of 15ft.
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the radius of the tank 6/2 = 3 ft
a. What is the volume of liquid in cubic feet if we fill the tank to one foot high?
 =
V = 28.274 cu/ft
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b. What is the total volume of the tank in cubic feet?
V = 424.114 cu/ft
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c. What is the volume of water in cubic ft in the tank if a measure stick indicates the water surface is 6 feet below the top of the tank?
15 - 6 = 9 ft is the height of the water
V = 254.469 Cu/ft of water
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d. What is the weight in pounds of the tank, as in the above case, if the tank itself weighs 20 lbs per ft of height?
We know that 1 cu/ft of water weighs 62.3 lb at 70 degrees
tank weight 20 * 15 = 300 lb
water weight 254.469 * 62.3 = 15,853.42 lb
Together they weigh: 16,153.42 lb
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e. How much water in gallons would have to be removed to reduce the total weight of the tank plus water, as in the above case, by 20%?
Find 20% of the weight of the above: .20(16158.42) = 3230.68 lb
1 gal weighs 8,34 lb
 = 387.37 gal should be removed to reduce the total weight by 20%
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f. What would be the new level of the water, as measured from the top of the tank, if the water in the above case (equivalent of 20% of total weight) is removed?
Change gal to cu/ft: .1337 * 387.37 = 51.79 cu/ft
Find the height of that much water in this tank
h = 1.8l3 ft
that would be
15 - 6 - 1.83 = 7.17 ft from the top of the tank
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You check my math on each of these question, it will confirm what I calculated and familiarize you with concepts we used in this lengthy problem. CK
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