Question

589 cubic meters of water is inside the 3,260 cubic meter spherical container. If the water inside the sphere is shaped as a spherical segment with the height of the water level equal to 5.25 meters, compute the upper radius (r) of the spherical segment

Answer 1

Volume of sphere, V=(4/3)πr³ so r³=3V/(4π) and r=∛(3V/(4π)) where r=radius. From this, r=9.1983m approx given V=3260 cubic metres.

If h=depth of water then r-h is the distance between the centre of the sphere and the surface of the water.

So, by Pythagoras, a, the radius of the water’s circular surface=√(r²-(r-h)²)=√(h(2r-h)).

Put r=9.1983 and h=5.25, a=8.3078m approx.

I’m puzzled about this because the water level should be about 4.98m not 5.25m. It wasn’t necessary to specify both the height and volume of water (?) Am I missing something?