Question

Two cubes have Volumes in the ratio 1 : 27. Find the ratio of their Surface Areas?
1. 1 : 9
2. 1 : 8
3. 1 : 18
4. 1 : 3

Answer 1

Correct Answer - Option 1 : 1 : 9

Given:

Ratio of volume of cube = 1 : 27

Formula used:

Volume of cube = a³

Surface area of cube = 6a²

Calculation:

Let the sides of two cubes be a₁ and a₂ respectively

Then, (a₁)³ : (a₂)³ = 1 : 27

⇒ a₁ : a₂ = 1 : 3

Ratio of surface areas = 6(a₁)² : 6(a₂)²

⇒ (a₁)² : (a₂)²

⇒ 1² : 3²

⇒ 1 : 9

∴ The ratio of their surface areas is 1 : 9