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Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the (i) radius r′ of the new sphere.

Q : 9    Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area \small S'. Find the

            (i) radius \small r' of the new sphere

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Given,

The radius of a small sphere = r

The radius of the bigger sphere = r'

\thereforeThe volume of each small sphere= \frac{4}{3}\pi r^3

And, Volume of the big sphere of radius r'\frac{4}{3}\pi r'^3

According to question,

27\times\frac{4}{3}\pi r^3=\frac{4}{3}\pi r'^3

\\ \Rightarrow r'^3 = 27\times r^3 \\ \Rightarrow r' = 3\times r

\therefore r' = 3r

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