Question

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

• A. $3:1$
• B. $2:3$
• C. $1:3$
• D. $9:1$

Answer 1

The correct option is A $3:1$

Let $x_1$ and $x_2$ be the edges of two cubes.

Given $\frac{V_1}{V_2}=\frac{27}{1}\Rightarrow \frac{(x_1{)}^3}{(x_2{)}^3}=\frac{27}{1}\Rightarrow {\left(\frac{x_1}{x_2}\right)}^3=\frac{27}{1}\Rightarrow \frac{x_1}{x_2}=\sqrt[3]{3\frac{27}{1}}=\frac{3}{1}$
$\Rightarrow x_1:x_2=3:1$