Q. 113.5( 11 Votes )

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

Answer :

Given,


Radius of the spherical ball = 3 cm


After recasting the ball into three spherical balls;


Radius of the first ball = r1 = 1.5 cm


Radius of the first ball = r2 = 2 cm


Let the radius of the third ball be r3 cm.


Then,


Volume of third ball = Volume of spherical ball – volume of 2 small balls


Volume of the third ball = π × 33 π π × 23


36π – – 32π/3cm3 = 125π/6cm3


4/3πr3 = 125π/6


r3 = 125π × 3/6 × 4 × π = 125/8


r = = 2.5 cm


Hence, the radius of the third ball is 2.5cm.


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