"A Spherical tank of radius 10 is full of liquid of density (omega) lb/ft^3. Find the work W done by pumping the liquid to the top of the tank."

Here's what I know: W=F*d. radius is 10 feet, and since the tank is half full, I can probably assume distance d would also be 10 feet. I also know the volume of the cylinder, which is pi*r^2*h. Using integration via cylinders, I's probably assume h is either dx or x. If it's dx (thickness), then the displacement d would actually be x, at which point I'm integrating from 0 to 10 (setting center of sphere as the origin).

Question

"A Spherical tank of radius 10 is full of liquid of density (omega) lb/ft^3. Find the work W done by pumping the liquid to the top of the tank."

Here's what I know: W=F*d. radius is 10 feet, and since the tank is half full, I can probably assume distance d would also be 10 feet. I also know the volume of the cylinder, which is pi*r^2*h. Using integration via cylinders, I's probably assume h is either dx or x. If it's dx (thickness), then the displacement d would actually be x, at which point I'm integrating from 0 to 10 (setting center of sphere as the origin).

anonymous · Answer

This would mean that my answer would be something along the lines of...

$$\int\limits_{0}^{10} \pi(10)^2xdx$$

My question is, did I get anything wrong here?

anonymous · Answer

Oh wait, forgot the omega:

$$\int\limits_{0}^{10} \pi(10)^2\omega*xdx$$

anonymous · Answer

SO yeah, did I get any part of that wrong?

anonymous · Answer

I'm studying for an exam, so my grade could potentially be riding on whether I get confirmation on this.