Question

The square on the diagonal of a cube has an area of 1875 cm2. Calculate the side of the cube and the total surface area of the cube?

Answer 1

Let the edge of the cube be a cm.

We know that, length of diagonal of the cube =

∴ Length of diagonal of the cube =a cm

The side of the square is equal to the length of diagonal of the cube. 

Area of square drawn on the diagonal of the cube == 3a2 cm2  [Area of the square = (side)2]

∴ 3a2 = 1875cm2  (Given)

⇒ a2 = 625cm2 = (25cm)2

⇒ a = 25cm

Edge of the cube =  a = 25cm

Total surface area of the cube = 6a2 = 6 × (25cm)2 = 5 × 625cm2  = 3750 cm2

Answer 2

1--------If the side of the cube = a cm,
the length of its diagonal = a^3 cm
{ a(cube root (3)) ^ 2 = 1875
a=25 cm
2-------6*(a^2)=6*625=3750 cm^3