A spherical ball of radius 3 cm is melted and recast into three spherical balls.

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asked Mar 27

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

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answered Mar 27 by (-3,089 points)

The radius of spherical ball = 3 cm

Volume of spherical ball = 4/3πr3

= 4/3π × 3 × 3 × 3

= 36π cm3

∵   Volume of spherical ball = Total volume of three small spherical ball

∵     The radii of the ball are 1.5 cm and 2 cm

∴  Let the radius of third ball = r

∴   Volume of spherical ball = Total volume of three small spherical balls

36π = 4/3π × (3/2)3 + 4/3π × (2)3 + 4/3 πr3

36π = 4/3π × 27/8 + 4/3π × 8 + 4/3πr3

36π = 4/3π(27/8 + 8 + r3)

(36π × 3)/4π = 27/8 + 8 + r3

27 = (27 + 64)/8 + r3

27 = 91/8 + r3

27 – 91/8 = r3

(216 – 91)/8 = r3

125/8 = r3

r = 5/2 cm

The diameter of the third ball = 2r = 2 × 5/2

= 5 cm

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