Option 4 : 9 : 25

Given

Ratio of volume of two spheres = 27 : 125

Formula used

surface area of sphere =4πr2

Volume of sphere = (4/3)πr3

Where r is radius respectively

Calculation

[(4/3)πR3/(4/3)πr3] = 27/125

Where R and r are radius of two sphere

⇒ R3/r3= 27/125

⇒ R = 3r/5

Surface area of 1st sphere/Surface area of 2nd sphere =[4π(3r/5)2]/4πr2

⇒ 9 : 25

∴ Ratio of surface area of two spheres is 9 : 25.

__Shortcut Trick__

**Given:**

Volume ratio = 27 : 125

**Concept:**

The ratio volume of spheres is the cube of the ratio of the radius and the ratio of surface areas is the square of the ratio of radius.

**Calculation:**

Rdaius ratio = ^{3}√ 27 : ^{3}√ 125

⇒ 3 : 5

So, surface area ratio = 9 : 25

**∴ The ratio is 9 : 25**