Question

if length of diagonal of cube is 12√3find surface area and volume​

Answer 1

Answer:

So the fact that it has √3 in the question is definitely not an accident.

Consider a square. For a “unit” square ( ie side length = 1 ) , the length of the diagonal is sqrt(1^2 + 1^2) = √2. This means for a square of side length x, it’s diagonal length is x√2.

Similarly for a unit cube, the diagonal length is sqrt(1^2 + 1^2+ 1^2) = √3, and for a cube of side length x, it’s diagonal length is x√3.

In fact it is not a big step to say that for any N dimensional cube of side length x, the length of the diagonal will be x√N.

Anyway, in this case, the side length is therefore 6, and the surface area is 6x^2 = 6 x 6^2 = 216 cm^2.