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 = r_{1} = 1.5 cm

Radius of the first ball = r_{2} = 2 cm

Let the radius of the third ball be r_{3} cm.

Then,

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

Volume of the third ball = π × 3^{3} – π – π × 2^{3}

36π – – 32π/3cm^{3} = 125π/6cm^{3}

4/3πr^{3} = 125π/6

r^{3} = 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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