Question

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

Answer 1

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Answer 2

Answer:

The diameter of the third ball is 5 cm.

SOLUTION :

Given :  

Let the Radius of the third ball be r3

Radius of the spherical ball , R = 3 cm

Radius of the first ball, r1 = 1.5 cm

Radius of the second ball, r2 = 2 cm

Volume of the spherical ball, V =  4/3πR³

Volume of the spherical ball is equal to the volume of the 3 small spherical balls.

Volume of the spherical ball, V = Volume (V1) of first ball + Volume (V2) of second ball + Volume of third ball (V3)

4/3πR³ = 4/3πr1³ + 4/3πr2³ + 4/3πr3³

4/3πR³ = 4/3π (r1³ + r2³ + r3³)

R³ = (r1³ + r2³ + r3³)

3³ = (1.5³ + 2³ + r3³)

27 = 3.375 + 8 + r3³

27 = 11.375 + r3³

r3³ = 27 - 11.375

r3³ = 15.625

r3 = ³√15.625

r3 = ³√ 2.5 × 2.5 × 2.5

r3 = 2.5 cm

Radius of the third ball = 2.5 cm

Diameter of the third ball = 2 × r3 = 2 × 2.5 = 5 cm

Diameter of the third ball = 5 cm

Hence, the diameter of the third ball is 5 cm.

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