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A solid spherical ball of iron with radi...

A solid spherical ball of iron with radius 6 cm is melted and recase tin to three solid spherical balls . The radii of the two of the balls are 3 cm and 4 cm respectively determine the diameter of the third ball.

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The correct Answer is:
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Let the radius of l third ball =r cm
The volume of three balls formed = volume of the ball melted
`(4)/(3)pi(3)^(3)+(4)/(3)pi(r )^(3)=(4)/(3)pi(6^(3))`
`27+64+r^(3)`=216
`r^(3)+64+r^(3)=216`
`r^(3)=125 i.e,r=5cm`
The diameter of the third ball =`2xx5`cm =10 cm
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