Question

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

(a) $1:3$

(b) $1:9$

(c) $1:27$

(d) none of these

Answer 1

Ratio in the two volumes $=1:27$

Let side of first cube $=x$

Therefore, volume of first cube $=x^3$

Hence, volume of second cube $=27x^3$

Thus, side of the second cube $=\sqrt[3]{327x^3}=3x$

Now, ratio of their surface areas is,

$=\frac{\text{Surface area of first cube}}{\text{Surface area of second cube}}$

$=\frac{6x^2}{6(3x{)}^2}$ [Surface area of $a$ sided cube is $6a^2$]

$=\frac{6x^2}{6\times 9x^2}=\frac{1}{9}$

$\therefore$ Required ratio $=1:9$