Question

A cube of edge 'k' is divided into 'n' equal cubes. What is the edge of the new cube?

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

Answer 1

The correct option is B

$\frac{k}{\sqrt[3]{3n}}$

Volume of cube with edge $k=k^3$
Volume of each smaller cube with edge = (let x) = $x^3$
No. of smaller cubes = n
As the total volume remain unchanged ,
Vol. of cube with edge k = (number of smaller cubes) x (Volume of each smaller cube with edge x)
$\Rightarrow k^3=n{x}^3\Rightarrow x^3=\frac{k^3}{n}\Rightarrow x=\sqrt[3]{3\left(\frac{k^3}{n}\right)}\Rightarrow x=\left(\frac{k}{n^{(}\frac{1}{3})}\right)$
So, the edge of new cube = $\frac{k}{n^{\left(1/3\right)}}$