Question

If the volumes of two cubes are in the ratio of 729 ∶ 512, then what is the ratio of their total surface area?
1. 36 : 49
2. 81 : 64
3. 25 : 36
4. 81 : 49

Answer 1

Correct Answer - Option 2 : 81 : 64

Given:

Cubes ratio = 729 ∶ 512

Formula used:

The volume of cubes = a³

The total surface area of the cube = 6a²

Where, a = Side of the cube

Calculation:

Let the side of the cubes are x and y respectively

According to the question,

x³/y³ =  729 ∶ 512

⇒ x/y = 9/8

⇒ x = (9/8)y

The Ratio of total surface area = 6x² ∶ 6y²

⇒ 6 × (9y/8)² ∶ 6y² 

⇒ (81/64) ∶ 1

⇒ 81 : 64

∴ The required ratio of the total surface area is  81 : 64.