Question

A cube of edge ' $k$ ' is divided into ' $n$' equal cubes. Determine the edge of the new cube

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

Answer 1

The correct option is B

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

Step 1: Given data

Edge of bigger cube$=k$

After dividing the bigger cube into smaller ones,

Number of smaller cubes $=n$

Edge of smaller cube,$k_s=?$

Step 2: Calculating the edge of smaller cube

Volume of cube$={\left(side\right)}^3$

As per the given data,

Volume of bigger cube$=n\times$Volume of smaller cube

$$\begin{gathered} k^3=n\times {\left(k_s\right)}^3 \\ \Rightarrow {\left(k_s\right)}^3=\frac{k^3}{n} \\ \Rightarrow k_s=\frac{k}{\sqrt[3]{n}} \end{gathered}$$

Hence, the edge of smaller cube will be $\frac{\mathrm{k}}{\sqrt[3]{\mathrm{n}}}$

Hence, option B is correct.