Question

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

Answer 1

Consider r cm as the radius of the third ball

We know that

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

It can be written as

4/3 π (27) = 4/3 π (27/8) + 4/3 π (8) + 4/3 πr³

Dividing the entire equation by 4/3 π

27 = 27/8 + 8 + r³

On further calculation

r³ = 27 – (27/8 + 8)

By taking LCM

r³ = 27 – ((27 + 64)/ 8)

So we get

r³ = 27 – (91/8)

By taking LCM

r³ = (216 – 91)/ 8 = 125/ 8

By taking cube root

r = 5/2 = 2.5 cm

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