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# 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? - CBSE Class 10 - Mathematics

ConceptVolume of a Combination of Solids

#### 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

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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Solution 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? Concept: Volume of a Combination of Solids.
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