Question

65. 27 solid iron spheres, each of radius 2 cm are melted to form a new solid sphere. What will be the surface area of the new sphere?​

Answer 1

Answer:

Radius of 1 solid iron sphere =r

⇒Volume =  $\frac{4}{3}$ πr³

⇒Volume of 27 solid iron spheres =27×  $\frac{4}{3}$ πr³

 ⇒$\frac{4}{3}$ πr'³ = 27×  $\frac{4}{3}$ πr³

πr'³ = 2πr³

⇒r' = 3r

⇒Surface Area = 4πr²

⇒ SA r' = 4πr'²

⇒ 4π(3r)² = 36πr²

⇒ $\frac{S}{S'}$ =  4πr² / 36πr²

       =  1/9

       = 1 : 9