Twenty seven solid iron spheres, each of radius r and surface area S are melted toform a sphere with surface area `\ Sprimedot`Find the(i) radius `rprime`of the new sphere, (ii) ratio of `S a n d Sprimedot`

Explanation

To solve the question, we need to find the radius of the new sphere formed by melting 27 solid iron spheres, each with radius \( r \) and surface area \( S \). We will also find the ratio of the surface area \( S \) of the smaller spheres to the surface area \( S' \) of the new sphere.

### Step-by-Step Solution:

1. **Calculate the Volume of One Iron Sphere:**
The volume \( V \) of a sphere is given by the formula:
\[
V = \frac{4}{3} \pi r^3
...