# Work problem

Homework Statement
Find the work required to empty a tank in the shape of a hemisphere of radius $$R$$ meters through an outlet at the top of the tank. The density of water is $$p kg/m^{3}$$; the acceleration of a free falling body is $$g$$. (Ignore the length of the outlet at the top.)

The attempt at a solution

$$w = \int_a^b (density)(gravity)(Area-of-slice)(distance)dx$$

$$w = \int_0^R (p)(g)(\pi)(R^{2})(R - x)dx$$

Is this correct/complete?

tiny-tim
Homework Helper
Hi Precursor! (have a pi: π and a rho: ρ and an integral: ∫ and try using the X2 tag just above the Reply box )
Find the work required to empty a tank in the shape of a hemisphere of radius $$R$$ meters through an outlet at the top of the tank. The density of water is $$p kg/m^{3}$$; the acceleration of a free falling body is $$g$$. (Ignore the length of the outlet at the top.)

$$w = \int_0^R (p)(g)(\pi)(R^{2})(R - x)dx$$

Is this correct/complete?

No, that's the correct formulal for a cylinder (Area-of-slice = πr2).

Try again! So is the area of the slice actually π(1 - x²)?

tiny-tim
Homework Helper
So is the area of the slice actually π(1 - x²)?

Nooo (btw, it might be easier if you measured x from the top instead of from the bottom )

Is it π√(R² - x²)?

tiny-tim
With x is measured from the top, yes except …
lose the square-root! 