Question

Two cubes have volumes in the ratio $1:64$. The ratio of their sides is ____.

• A. $1:3$
• B. $1:4$
• C. $1:8$
• D. $8:1$

Answer 1

The correct option is B $1:4$

Given:
Volume ratio of two cubes is $1:64.$

Let side length of cube 1 be $a_1.$
Let side length of cube 2 be $a_2.$

Volume of cube 1 will be:
$V_1=a_1^3$
Volume of cube 2 will be:
$V_2=a_2^3$

Ratio of volumes is:
$\frac{V_1}{V_2}=\frac{a_1^3}{a_2^3}$
$\frac{1}{64}={\left(\frac{a_1}{a_2}\right)}^3$
$\frac{a_1}{a_2}=\frac{1}{4}$

Therefore, ratio of their sides is 1 : 4.