Question
If three metallic spheres of radii 6 cms and 10 cms are melted to from a single sphere , the diameter of the new sphere will be :
Answer: Option B
= `(4/3 pi xx 1728) cm^3`
= `[4/3 pi xx (12)^3] cm^3`
Let he radius of he new sphere be R. Then ,
`4/3 pi R^3 = 4/3 pi xx (12)^3`
`hArr R^3 = (12)^3`
`rArr R = 12 cm`
`:.` Diameter = 2R = 24 cm.
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Volume of new sphere = `[ 4/3 pi xx (6)^3 + 4/3 pi xx (8)^3 + 4/3 pi xx (10)^3] cm^3`
= `{4/3 pi [(6)^3 + (8)^3 + (10)^3]} cm^3`= `(4/3 pi xx 1728) cm^3`
= `[4/3 pi xx (12)^3] cm^3`
Let he radius of he new sphere be R. Then ,
`4/3 pi R^3 = 4/3 pi xx (12)^3`
`hArr R^3 = (12)^3`
`rArr R = 12 cm`
`:.` Diameter = 2R = 24 cm.
Was this answer helpful ?
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