Question

If the volume of a cube is $192\sqrt{3}$ cubic cm, then the length of its diagonal is:

• A. 16 cm
• B. 14 cm
• C. 13 cm
• D. 12 cm

Answer 1

Answer:

D. 12 cm

Solution:

Given:

Volume of cube = 192√3 cubic cm

Formula used:

Volume of cube = a³

Where a = side of the cube

Length of the diagonal of the cube = √3 × a 

Calculation:

Let the side of the cube be 'a' cm

Volume = 192√3 

⇒ a³ = 192√3 

⇒ a = (192√3)^1/3 = (4 × 4 × 4 × 3 × √3)^1/3

⇒ a = 4 × (3√3)^1/3 

Diagonal of the cube = √3 × a 

⇒ √3 × 4 × (3√3)^1/3

⇒ √3 × 4 × [(√3)³]^1/3

⇒ 12 cm

∴ The length of the diagonal of the cube is 12 cm.