Correct Answer - Option 2 : 9 : 25
Given:
The ratio of the volume of the cube = 27 : 125
Formula used:
The volume of cube = a3
The surface area of cube = 6a2
Calculation:
Let the sides of two cubes be a1 and a2 respectively
Then, (a1)3 : (a2)3 = 27 : 125
⇒ a1 : a2 = 3 : 5
The ratio of their of surface areas = 6(a1)2 : 6(a2)2
⇒ (a1)2 : (a2)2
⇒ 32 : 52
⇒ 9 : 25
∴ The ratio of their surface areas is 9 : 25
