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, (ii) ratio of S and S′.
Solution (i)
Twenty seven solid iron spheres, each of radius r, are melted to form a bigger sphere of radius r’. It means that combined volume of 27 spheres is equal to volume of new sphere.
Therefore, 27
(volume of 1 sphere of radius r) = Volume of new sphere of radius r’
Solution (ii)
Surface area of smaller sphere
Surface area of new sphere
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