a spherical ball of lead 3 cm in diameter is melted..., Area & Volume, General Mathematics

Question:A spherical ball of lead, `3` cm in diameter is melted and recast into three spherical balls. The diameter of two of these are `1.5` cm and `2` cm respectively. The diameter of the third ball is :

A `2.66 cm` 
B `2.5 cm` 
C `3 cm` 
D `3.5 cm`

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+ AnswerB

+ Explanation`4/3 π xx (3/4)^3 + 4/3 π xx (1)^3 + 4/3 π xx x^3`

`= 4/3 π xx (3/2)^3`

`or 27/64 + 1 + x^3`

`= 27/8`

`or x^3 = 125/64`

`= (5/4)^3`

`or x = 5/4.`

:. Radius of the third ball is `5/4 cm`.

Hence, the diameter of this ball is `5/2 cm = 2.5 cm.`

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