Work Prob.: A hemispherical tank with radius 5 ft is filled

[flakine]

A hemispherical tank with radius of 5 ft is filled with water. Given that water weights 62.5 lb/ft^3, find the work required to pump the water out of the top of the tank.

How would I set this one up?

 

[stapel]

How would I set this one up?

You would probably want a set-up similar to the other work problems you've posted.

Eliz.

 

[flakine]

These problems are very different. The only similarity is integration. I'm perparing for a test and need to know if I'm setting these types of problem up correctly.

Is this correct: 62.5pi * the integration of (25-x^2)(5-x) from a=0, b=5

 

[galactus]

\(\displaystyle \L\\62.5{\pi}\int_{-5}^{0}(-y)(25-y^{2})dy\)

\(\displaystyle \L\\=62.5{\pi}\int_{-5}^{0}(y^{3}-25y)dy\)

Let the top of the tank on the flat surface be the origin.

Therefore, the volume of the kth slice is \(\displaystyle {-}y(25-y^{2})\)