Question

The radius of a solid mettalic sphere is 8 cm. The sphere is melted and recast into eight equal solid spherical ballsv. Determine the diameter of balls

Answer 1

radius of bigger sphere = 8 cm
Its volume = 4/3 pi r^3
= 4/3 pi 8^3
= 4/3×pi×8×8×8

Let the radius of the smaller balls be r
Therefore, Volume of one such small ball
= 4/3×pi×r^3

And then ; the volume of 8 such balls
= 8 × 4/3×pi×r^3

Given that the big sphere is melted to eight small spheres
Therefore,

Volume of the big sphere = Volume of eight small spheres

4/3×pi×8×8×8 = 8 × 4/3×pi×r^3
=> ( 4/3 and pi get cancelled )
8×8×8 = 8 × r^3
8×8 = r^3
64=r^3
=> r = 4 cm

Therefore the diameter of the smaller balls = 2r = 2×4 = 8cm
Ans : 8 cm

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