#### Question

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

#### Solution

Given that a spherical ball of radius 3cm

We know that Volume of a sphere`=4/3pir^2`

So its volume(v)`=4/3pi(3)^2`

Given that ball is melted and recast into three spherical balls

Radii of first ball (v_{1})=`4/3pi(1.5)^3`

Radii of second ball(v_{2})=`4/3pi(2)^3`

Radii of third ball ___________?

Volume of third ball `=4/3pir^3=v_3`

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

⇒ `4/3pir^2+4/3pi(1.5)^3+4/3pi(2)^3=4/3pi(3)^3`

⇒ `r^2+(1.5)^3+(2)^3=(3)^3`

⇒ `r^3=3^3-1.5^3-2^3`

⇒ `r-(15.6)1/3`

⇒ `r=2.5cm`

Diameter (d) = 2r = 2 x 2.5 = 5cm

∴Diameter of third ball = 5cm.