Question

The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.

Answer 1

Let the radius of two spheres be r₁ and r₂.

Given, the ratio of the volume of two spheres = 64 : 27

i.e., `V_1/V_2 = 64/27`

⇒ `(4/3 pir_1^3)/(4/3 pir_2^3) = 64/27`

⇒  `(r_1/r_2)^3 = (4/3)^3`   ...`[∵ "Volume of sphere" = 4/3 pir^3]`

⇒ `r_1/r_2 = 4/3`

Let the surface areas of the two spheres be S₁ and S₂.

∴ `S_1/S_2 = (4pir_1^2)/(4pir_2^2) = (r_1/r_2)^2`

⇒ `S_1 : S_2 = (4/3)^2 = 16/9`

⇒ S₁ : S₂ = 16 : 9

Hence, the ratio of their surface areas is 16 : 9.