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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 (v1)=`4/3pi(1.5)^3`
Radii of second ball(v2)=`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.
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