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 i) Radius r’ of the new sphere ii) ratio of S and S’

The correct answer is: 1:9

Explanation:

• We have given twenty seven solid iron spheres , each of radius r and surface area S are melted to form a sphere with surface area S’.
• We have to find the Radius of new sphere and the ratio of S and S’

Step 1 of 2:
We have given 27 solid spheres each of radius r and surface area s
So,
(i)
Volume of each sphere will be

Volume of big sphere

So,


Step 2 of 2:
Surface area is 
 and


Therefore,

= 
Or
1 : 9