maths

A spherical tank in a petro-chemical plant has a radius of 5m.
Give an expression which, when integrated from y=-r to
y=d-r ,will give the volume of liquid in the tank where r is
the radius and d is the depth of liquid.
If liquid is entering the tank at a rate of 1500 litres per second and
the depth is 3m how long will it take to fill the tank? Give your
answer in seconds.

asked by URGENT
  1. The volume of a thin slice of water is the area of the slice times its thickness, dy

    At a depth of d, with d<r, we have
    the radius of the surface of the water is x = √(r^2-y^2)
    v = ∫[-r,d-r] π(r^2-y^2) dy

    Now you can answer the last part by subtracting the volume from the whole sphere's volume of 4/3 pi * 5^3 and dividing by 1500L/s = 1.5 m^3/s

    posted by Steve

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