Question

64 solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the ratio of S and S​

Answer 1

Answer:

The ratio of S and S'  = 1 : 16  

Step-by-step explanation:

Given data

64 solid iron spheres, each of radius is r and surface area is S

and 64 spheres are melted to form a large sphere which have surface area S'

here we need to find ratio of S and S'

Area of small solid sphere S = 4$\pi$$r^{2}$  

Area of sphere which is made from 64 solid spheres

                                           S' = 64 × 4$\pi$$r^{2}$

ratio of S and S' = 4$\pi r^{2}$ : 64×4$\pi$$r^{2}$  

                           = 4 : 64 [divided by 4$\pi$$r^{2}$  and 4]

                           = 1 : 16

⇒ The ratio of S and S'  = 1 : 16