A spherical ball is immersed in water contained in a vertical cylinder. The rise in water level is measured in order to calculate the radius of the ball. Calculate the radius of the ball in the following cases:

(a) : cylinder of radius 10cm, water level rises 4cm.

(b) : cylinder of radius 100cm, water level rises 8cm

Immersed = > totally submerged

a) Volume occupied by the ball, V = area of the base of the cylynder * water level rise

V = π (r^2) (4cm) = π*100cm^2*4cm = 400 π cm^3

Volume of a sphere = [4/3]π (r^3) = 400 π cm^3 = >

r^3 = 300 cm^3 = > r = ∛ (300 cm^3) = 6.69 cm

b) V = π (100cm) ^2 (8cm) = 80,000 π cm^3

[4/3]πr^3 = 80,000π cm^3 = > r^3 = 60,000 cm^3 = > r = 39.15 cm