Question

Sixty four solid iron spheres, each of radius r and surface area S are melted to form a sphere with surad S. Find the ratio of S and S'.​

Answer 1

volume of 64 iron spheres=volume of new sphere

64×4/3πr³=4/3πr'³

64r³=r'³

³√64r³=³√r'³

4r=r'

r'=4r

ratio of s and s'

s/s'=4πr²/4πr²

=(r²)/(4r')²

=r²/16r²

=1/16