Answer to Question #140617 in Physics for Samuel

Question

A tank is a vertical cylinder with inside diameter of 6ft and a height of 15ft.
(a). What is the weight in pounds of the tank, if the tank itself weighs 20lbs per ft of height.
(b). How much water in gallons would have to be measured to reduce the total weight of the tank plus water in the above case by 20%.
(c). What would be the new level of the water as measured from the top of the water if the water in the above case (equivalent of 20% of total weight) is removed.
(d). What is the volume of liquid is cube feet if we fill the tank to 1ft high.
(e). What is the total volume of the tank in cube feet.
(f). What is the volume of the water in cube ft in the tank if a measure stick indicates the water surface is 6ft below the top of the tank.

Answer 1

a)

$$W=(20)(15)+0.25\pi(6)^2(15)(62.3)=26722\ lb$$

b)

$$(20)(15)+V(62.3)=(0.8)26722\\V=338.3\ ft^3=2530839\ gal$$

c)

$$0.25\pi(6)^2(62.3)h=(0.2)26722\\h=3.0\ ft$$

d)

$$V=0.25\pi(6)^2(1)=28.3\ ft^3$$

e)

$$V=0.25\pi(6)^2(15)=424.1\ ft^3$$

f)

$$V=0.25\pi(6)^2(15-6)=254.5\ ft^3$$