Two cubes have their volumes in the ratio 1:27. The ratio of their surface areas is
Given: Volumes of the cubes are in the ratio 1:27.
Volume of a cube is given by: a3 ( here ‘a’ is the side of the cube).
Surface are of a cube is given by: a2 ( here ‘a’ is the side of the cube).
Let a1, a2 be the side of first cube and second cube respectively.
∴ (a1)3: (a2)3 = 1:27
⇒ a1: a2 = ∛1 : ∛27
⇒ a1: a2 = 1 : 3
⇒ (a1)2: (a2)2 = 12: 32
⇒ (a1)2: (a2)2 = 1 : 9
∴ Ratio of the surface areas of the given cubes is 1:9.