Question

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

• A. 3 : 1
• B. 27 : 1
• C. 1 : 27
• D. 1 : 9

Answer 1

The correct option is A 3 : 1

Let $V_1,V_2$ be the volumes and $a,b$ be the edges of cube 1 and cube 2 respectively.

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

Volume of a cube is equal to the cube of its edge.

$\frac{V_1}{V_2}=\frac{a^3}{b^3}=\frac{27}{1}$
$\frac{a}{b}={\left(\frac{27}{1}\right)}^{\frac{1}{3}}$
$\frac{a}{b}=\frac{3}{1}$

The ratio of their edges is 3 :1.