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,
a³/b³ = 1/27
⇒ (a/b)³ = (1/3)³
⇒ a/b = 1/3 -------------------- (1)
Therefore, Ratio of the surface area,
⇒ 6a²/6b²
⇒ a²/b²
⇒ (a/b)²
⇒(1/3)² [From (1)]
⇒1/9
⇒i.e. 1 : 9
Ratio of the surface area = 1 : 9