Question

If the volume of a cube is 64 cm³, then the diagonal of cube is

• A. 4 cm
• B. $4\sqrt{3}$ cm
• C. $\sqrt{3}$ cm
• D. $\frac{4}{\sqrt{3}}$ cm

Hint:

Cube volume = $a^3$. Diagonal length = side length × $\sqrt{3}$. Use these formulas to quickly find missing measurements.

Answer 1

The Correct Option is B

The volume $V$ of a cube is given by $V = a^3$, where $a$ is the side length. Given that $V=64$ cm³, \[ a = \sqrt[3]{64} = 4 \text{ cm}. \] The diagonal $d$ of a cube is the space diagonal, which can be found using the Pythagorean theorem in three dimensions: \[ d = a \sqrt{3} = 4 \sqrt{3} \text{ cm}. \] This diagonal represents the longest distance between two opposite vertices of the cube.