Question

What's the ratio of the lateral surface areas of the cubes if
$\frac{l_1}{l_2}=\frac{1}{2}?$
[$l_{1}and{l}_2$ are the lengths of the sides of cubes]

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $\frac{1}{4}$

Lateral surface area of the cube is
$4\times (side{)}^2$

Let $l_1$ and $l_2$ be the lengths of the sides of the cubes ${\text{cube}}_1$ and ${\text{cube}}_2$ respectively.

Given, $\frac{l_1}{l_2}=\frac{1}{2}$.

Now,
$\text{Required ratio}=\frac{{\text{lateral surface area of cube}}_1}{{\text{lateral surface area of cube}}_2}=\frac{4\times (l_1{)}^2}{4\times (l_2{)}^2}=(\frac{l_1}{l_2}{)}^2=(\frac{1}{2}{)}^2=\frac{1}{4}$