Question

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

(a) 1 : 3 (b) 1 : 8 (c) 1: 9 (d) 1 : 18

Answer 1

Let their edges be a and b.
Then,
$\frac{a^3}{b^3}$ = $\frac{1}{27}$
⇒ $(\frac{a}{b}{)}^3$ = $(\frac{1}{3}{)}^3$
⇒ $\left(\frac{a}{b}\right)$ = $\left(\frac{1}{3}\right)$ -------------------- (1)
Therefore, Ratio of the surface area,
⇒ $\frac{6a^2}{6b^2}$
⇒ $\frac{a^2}{b^2}$
⇒ $(\frac{a}{b}{)}^2$
⇒$(\frac{1}{3}{)}^2$ [From (1)]
⇒$\left(\frac{1}{9}\right)$
⇒i.e. 1 : 9
Ratio of the surface area = 1 : 9

option (c)