Question 1088949
A tank is a vertical cylinder with inside diameter of 6ft and a height of 15ft.
:
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 = pi*3^2*1}}} = 
V = 28.274 cu/ft
:
 b. What is the total volume of the tank in cubic feet?
{{{V = pi*3^2*15}}}
V = 424.114 cu/ft
:
 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 = pi*3^2*9}}}
V = 254.469 Cu/ft of water
:
 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
:
 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
{{{3230/8.34}}} = 387.37 gal should be removed to reduce the total weight 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?
Change gal to cu/ft: .1337 * 387.37 = 51.79 cu/ft
Find the height of that much water in this tank
{{{pi*3^2*h = 51.79}}}
h = 1.8l3 ft
that would be
15 - 6 - 1.83 = 7.17 ft from the top of the tank
:
:
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