Question

Two cubes have their volumes in the ratio $1:27$. Find the ratio of their surface areas.

• A. $1:8$
• B. $1:9$
• C. $7:9$
• D. $2:5$

Answer 1

The correct option is B $1:9$

we know that the Volume of a cube is a cube of its side and the Surface area is six times its square of side.

Let $a_1,a_2$ be sides of two cubes.

$\Rightarrow V=a^3$ and Surface area $=6a^2$

Given, $V_1:V_2=1:27$

$\Rightarrow V_1:V_2=a_1^3:a_2^3$

$\Rightarrow a_1^3:a_2^3=1:27$

$\Rightarrow a_1:a_2=1:3$

$\Rightarrow a_1^2:a_2^2=1:3^2=1:9$

$S{a}_1:S{a}_2=6a_1^2:6a_2^2=a_1^2:a_2^2=1:9$

Therefore, the ratio of surface areas is $1:9$.

Option (B) is correct.