Question

a solid cube is cut into 27 small cubes of equal volumes.find the ratio of surface the surface areas of the given cube and that one small cube

Answer 1

We know that volume of cube = a^3.

Let the side of the larger cube be S and the smaller cube be s.

Given that a solid cube is cut into 27 small cubes of equal volumes.

⇒ (Side of big cube)^3 = 27 * (side of small cube)^3

⇒ (S)^3 = 27 * (s)^3

⇒ (S)^3/(s)^3 = 27/1

⇒ (S/s)^3 = 27/1

⇒ S/s = ∛27/1

⇒ S/s = 3/1

Now,

Ratio of surface area = 3^2/1^2

                                   = 9/1

                                   = 9 : 1.

Hope it helps!