# Thread: Help on emptying a tank of oil

1. ## Help on emptying a tank of oil

A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds per cubic foot.

Find the work required to pump oil out through a hole in the top of the tank.

Hints: Set the center of the sphere at (0,8) in a coordinate plane. Consider that a slice of the sphere is a circle.

A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds per cubic foot.

Find the work required to pump oil out through a hole in the top of the tank.

Hints: Set the center of the sphere at (0,8) in a coordinate plane. Consider that a slice of the sphere is a circle.

$\displaystyle W=F\cdot d$

$\displaystyle F=50V$
where V is the approxmation of the volume of one slice of oil.

I put the center of the sphere at (0, 0) so the radius of each slice is
$\displaystyle \sqrt{64-y^2}$

Then $\displaystyle V=\pi(\sqrt{64-y^2})^2\,dy$

$\displaystyle d=8-y$

So $\displaystyle W=\int_{-8}^0\pi(64-y^2)(8-y)\,dy$