Explanation:

According to the question
Radius of the spherical ball=3cm
We know that the volume of the sphere= (4/3)Πr³
So it’s volume (v)= (4/3)Πr³
Given,
That the ball is melted and recast into 3 spherical balls.
Volume (V1) of first ball = (4/3)∏1.5³
Volume (V2) of second ball = (4/3)∏2³
Radii of the third ball be =r cm
Volume of third ball (V3) = (4/3)∏r³
Volume of the spherical ball is equal to the volume of the 3 small spherical balls.
V=V₁+V₂+V₃
(4/3)Πr³= (4/3)∏1.5³+ (4/3)∏+2³+ (4/3)∏r³
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=15.6cm³
r= (15.6)? cm
r=2.5cm
we know diameter = 2* radius
=2*2.5 cm
=5.0 cm
The diameter of the third ball is 5.0 cm