Posted by **Jerry** on Wednesday, October 10, 2012 at 11:12am.

A spherical tank with radius of 5 feet is set on a coloumn 15 feet above the ground. How much work is required to fill the tank with water if the solution is pumped from ground level?

- Calculus II -
**Steve**, Wednesday, October 10, 2012 at 11:39am
Let the center of the tank be at (0,0)

when the water level is at y, the radius of the water surface is

r^2 = 25-y^2

Work is ∫F(y) dy

F(y) is the weight of the water. So, since each slice of water in the tank is raised 21+y feet, and water weighs 62.4 lbs/ft^3,

W(y) = ∫[-5,5] 62.4 π (25-y^2) (21+y) dy

= 218400π

## Answer this Question

## Related Questions

- math - A fish tank 1 feet x 1 1/2 feet x 1/2 feet is carefully used to fill a ...
- math - A cylindrical tank is lying horizontally on the ground, its diameter is ...
- AP calculus - The base of a cone-shaped tank is a circle of radius 5 feet, and ...
- Calculus - A cylindrical water tank has a radius of 2 feet and a height of 6.0 ...
- Calculus 2 - Calculus 2. Tom and Mike have a bet as to who will do the most work...
- Calculus (Definite Integrals - Work) - Recall that work is defined to be force ...
- Calculus - A spherical oil tank with a radius of 10 feet is half full of oil ...
- calculus - A conical water tank with vertex down has a radius of 12 feet at the ...
- Physics/Calculus - A spherical oil tank with a radius of 10 feet is half full of...
- Calculus (math) - A conical water tank with vertex down has a radius of 12 feet ...

More Related Questions