Question

If the volume of two cubes are in the ratio $27:1$, the ratio of their edges is :

• A. $3:1$
• B. $27:1$
• C. $1:3$
• D. $1:27$

Answer 1

The correct option is A

$3:1$

Step 1: Given data

As per the data given in the question,

We have,

Volume of two cubes are in the ratio $27:1$,

Let ${\mathrm{V}}_1,{\mathrm{V}}_2$ be the volumes and $a,b$ be the edges of cube $1$ and cube $2$ respectively.

Step 2: Determining the volume of cube

As we know that,

Volume of a cube $=(\text{edge}{)}^3$

Given: $\frac{V_1}{V_2}=\frac{27}{1}$

So,
$$\begin{gathered} \Rightarrow \frac{V_1}{V_2}=\frac{27}{1} \\ \Rightarrow \frac{a^3}{b^3}=\frac{27}{1} \\ \Rightarrow \frac{\mathrm{a}}{\mathrm{b}}={\left(\frac{27}{1}\right)}^{1/3} \\ \Rightarrow \frac{\mathrm{a}}{\mathrm{b}}=\frac{3}{1} \end{gathered}$$

$\therefore$ The ratio of edges of two cubes is $3:1$