Question

Find the ratio of the numerical value of volume and total surface area of a cube whose diagonal is 4√3 m.

1. 2 : 3
2. 3 : 4
3. 4 : 3
4. 4 : 5

Answer 1

Correct Answer - Option 1 : 2 : 3

Given:

Diagonal of the cube is 4√3 m

Concept Used:

Length of the diagonal of a cube of side ‘a’ unit is a√3 unit

The volume of a cube of side ‘a’ unit is a³ cube unit

If ‘a’ be the side of a cube then total surface area of the cube is 6a²

Calculation:

Let, the length of the side of the cube be a

Accordingly,

a√3 = 4√3

⇒ a = 4

Length of the side of the cube is 4 m

The volume of the cube is 4³ = 64 m³

The total surface area of the cube is 6 × 4² = 96 m²

The ratio of the numerical value of volume and total surface area is 64 : 96

⇒ 2 : 3

∴ The ratio of the numerical value of volume and total surface area is 2 : 3