Question

A cube of edge ‘k’ is divided into ‘n’ equal cubes. Determine the edge of the new cube.

• A. $\sqrt{nk}$
• B. $\frac{k}{\sqrt[3]{3n}}$
• C. $\sqrt[3]{3n}$
• D. $\frac{\sqrt[3]{3n}}{k}$

Answer 1

The correct option is B $\frac{k}{\sqrt[3]{3n}}$

Volume of the bigger cube is equal to the sum of the volumes of the smaller cubes formed.
We know, volume of a cube = $sid{e}^3$
Given, 'k' is the edge of bigger cube and it is divided into 'n' equal cubes.
$⟹k^3=n{k}_s^3,\text{where}{k}_s$ is the edge of the new cube.
$⟹k_s=\frac{k}{\sqrt[3]{3n}}$
$\therefore$ Edge of the new cube, $k_s=\frac{k}{\sqrt[3]{3n}}$