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 radius r of the new sphere. ratio of S and S.

Explanation

To solve the problem, we need to find the radius \( r' \) of the new sphere formed by melting 27 solid iron spheres, each with radius \( r \), and then determine the ratio of the surface areas \( S \) and \( S' \).

### Step-by-Step Solution:

1. **Surface Area of One Sphere**:
The surface area \( S \) of one sphere with radius \( r \) is given by the formula:
\[
S = 4\pi r^2
...