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, defined by the formula $V = a^3$ where $a$ is the side length, is given as $V=64$ cm³. Therefore, the side length is calculated as: \[a = \sqrt[3]{64} = 4 \text{ cm}.\] The space diagonal $d$ of the cube, representing the longest distance between opposite vertices, is determined using the three-dimensional Pythagorean theorem: \[d = a \sqrt{3} = 4 \sqrt{3} \text{ cm}.\]