Help me!!!! Arrhhhh (1 Viewer)

[Peek-a-boo!!!]

Hi evrione !!! Help me!!
the question is : A sphere of a radius r units is completely immersed in water contained in a tank with a square base. If the base edge of the tank is x units long, show that when the sphere is removed the fall in the water level is given by:

F=4 pi r cubed/3 x squared

How can i prove this. Serious help needed. Thank you

 

[Trev]

Volume of a sphere is (4/3)pi.r³
Volume of the tank is x³
You want to find the fall in the water level, the water level is originally 'x' units high, let the height when the sphere is removed be 'F'. Therefore, the change in water level will be 'x-F' units.
Volume taken away will be "x³-(4/3)pi.r³"; the volume taken away will also be the change in water level 'x-F' multiplied by base and width, x*x. So:
x³-(4/3)pi.r³=x²(x-F)
x-F = x - (4.pi.r³)/(3x²)
F = (4.pi.r³)/(3x²) as required.

 

[Peek-a-boo!!!]

Thanks lots for the answer. Yeah!! Yippee!!!!! I'm so happi. Thank you