If V₁, V₂ are volumes and S₁, S₂ are the surface areas of two cubes then

Given:

V₁, V₂ are the volumes of two cubes.

S₁, S₂ are the surface areas of two cubes.

Formula used:

Volume of a cube = (Side)³

⇒ V₁ = a₁³, V₂ = a₂³

Surface area of a cube = 6 × (Side)²

⇒ S₁ = 6a₁², S₂ = 6a₂²

Calculation:

Ratio of volumes:

⇒ V₁ / V₂ = (a₁ / a₂)³

Taking cube root on both sides:

⇒ (V₁ / V₂)^1/3 = a₁ / a₂

Ratio of surface areas:

⇒ S₁ / S₂ = (a₁² / a₂²)

Substituting a₁ / a₂:

⇒ S₁ / S₂ = (V₁ / V₂)^2/3

⇒ \(\rm \frac{s_1}{s_2}=\left(\frac{v_1}{v_2} \right)^{\frac{2}{3}}\)

∴ The required ratio of S₁ and S₂ is \(\rm \frac{s_1}{s_2}=\left(\frac{v_1}{v_2} \right)^{\frac{2}{3}}\).