calculus

A circular swimming pool has a diameter of 14 m, the sides are 4 m high, and the depth of the water is 3.5 m. (The acceleration due to gravity is 9.8 and the density of water is 1000 .)
How much work (in Joules) is required to:
(a) pump all of the water over the side?
(b) pump all of the water out of an outlet 2 m over the side

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  1. If you are at all smart, none.
    You siphon the water out.

    However if you really want to lift it all to the top then the answer is the mass of water times height you lift it times gravity ( m g h )

    Mass = m = pi (7)^2 (3.5)(1000) m^3

    g = 9.8 m/s^2

    h = 4 - (3.5)/2 = 2.25 m

    so multiply and get Joules
    for the second part use 2.25 + 2 = 4.25 for h

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