Q. 94.4( 230 Votes )

# 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′

Answer :

**(i)** Volume of new sphere having radius r’ = πr’^{3}

Volume of 27 spheres having radius r = 27 × πr^{3}

According to the question,

πr’^{3} = 27 × πr^{3}

= r’^{3} = 27r^{3}

= r’^{3} = (3r)^{3}

r’ = 3r

**(ii)** Ratio of surface area =

=

= = 1: 9

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