Question

twenty seven solid iron spheres each radius r and surface area s are melted to form a sphere with surface area S' find the

1) radius r' of the new sphere
2) ratio of S and S'

Answer 1

volume of 1 small sphere = 4/3pi*r3

volume of 27 such spheres= 27*4/3pi*r3 = 36pi*r3

volume of new sphere = volume of 27 small spheres

so , 4/3pi* r'^3 = 36pi*r^3

r'^3= 27r^3

r' = 3r...................(i)

now ratio of surface areas =

S/S' = 4pi*r^2 / 4pi*r'^2

but r' = 3r

therefore, S/S' = 4pi*r^2 / 4pi*(3r)^2

= r^2 / 9r^3

Hence, S/S' = 1/9 Ans.

I hope it will help u.....