Question

If diagonal of a cube is 9 dm.then, find the volume of a cube.
1. 343√3 dm³
2. 81√3 dm³
3. 46√3 dm³
4. 31√3 dm³

Answer 1

Correct Answer - Option 2 : 81√3 dm³

Formula used

Diagonal of a cube = √3(side)

Given

Diagonal of a cube = 9

Calculation

√3(side) = 9

Squaring on both sides

3(side)² = 81

⇒ (Side)² = 27

⇒ Side = √27

⇒ Side = 3√3 dm

Volume of a cube = (3√3)³

⇒ 81√3 dm³

∴ The volume of a cube is 81√3 dm³