Question

If the side of the cube is 6 cm, then the diagonal of the cube is:

• A. \( 3\sqrt{2} \, \text{cm} \)
• B. \( 6\sqrt{3} \, \text{cm} \)
• C. \( 6\sqrt{2} \, \text{cm} \)
• D. \( 2\sqrt{3} \, \text{cm} \)

Hint:

The diagonal of a cube with side length \( s \) is given by \( d = s\sqrt{3} \), derived from the Pythagorean theorem applied in three dimensions.

Answer 1

The Correct Option is B

For a cube with side length \( s \), the diagonal \( d \) can be found using the Pythagorean theorem in three dimensions: \[ d = \sqrt{s^2 + s^2 + s^2} = \sqrt{3s^2} = s\sqrt{3} \] Substituting \( s = 6 \, \text{cm} \): \[ d = 6\sqrt{3} \, \text{cm} \] Thus, the diagonal of the cube is \( 6\sqrt{3} \, \text{cm} \).