Question

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

Answer 1

Given,

Radius of the spherical ball = 3 cm

We know that,

The volume of the sphere = 4/3 πr³

So, it’s volume (V) = 4/3 πr³

That the ball is melted and recast into 3 spherical balls.

Volume (V₁) of first ball = 4/3 π 1.5³

Volume (V₂) of second ball = 4/3 π2³

Let the radius of the third ball = r cm

Volume of third ball (V₃) = 4/3 πr³

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

Now,

Cancelling out the common part from both sides of the equation we get,

(3)³ = (2)³ + (1.5)³ + r³

r³ = 3³– 2³– 1.5³ cm³

r³ = 15.6 cm³

r = (15.6)^1/3 cm

r = 2.5 cm

As diameter = 2 x radius = 2 x 2.5 cm

= 5.0 cm.

Thus, the diameter of the third ball is 5 cm