A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is k(kr)feet below the surface of the fluid. Show that the fluid force on the surface of the plate is F=wk(πr^2). How to prove this given formula by Evaluating one integral by a geometric formula and the other by observing that the integral is an odd function?

Question

A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is k(k>r)feet below the surface of the fluid. Show that the fluid force on the surface of the plate is F=wk(πr^2). How to prove this given formula by Evaluating one integral by a geometric formula and the other by observing that the integral is an odd function?