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

            (ii) ratio of S and \small S'.

Answers (1)
H Harsh Kankaria


The radius of a small sphere = r

The surface area of a small sphere = S

The radius of the bigger sphere = r'

The surface area of the bigger sphere = S'

And, r' = 3r

We know, the surface area of a sphere =4\pi r^2

\therefore The ratio of their surface areas = \frac{4\pi r'^2}{4\pi r^2}

\\ = \frac{ (3r)^2}{ r^2} \\ = 9

Therefore, the required ratio is 1:9