Question

Twp cubes have their volume in ratio 1:27.Find the ratio of their surface area.
Explain in detail.

Answer 1

Note;
consider a cube of side length =x
the volume of cube=x^3
and surface area of cube =6a^2
in these qustion


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

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