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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

Verified Answer :

Edufirst

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) = π100cm^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

 

 


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