Question

The square on the diagonal of a cube has an area 363 cm². Calculate the side and the surface area of the cube.

Answer 1

Step 1: Let the side of the cube be a cm

The diagonal of a cube is given by `d = asqrt(3)`

The square on the diagonal has an area equal to area of square = d²

We are given:

d² = 363 cm²

Step 2: Express d² in terms of a

`d = asqrt(3)`

⇒ `d^2 = 3a^2`

`3a^2 = 363`

`a^2 = 363/3 = 121`

`a = sqrt(121)`

a = 11 cm

Step 3: Find the surface area of the cube

Surface area of a cube: 6a²

6a² = 6 × 121 = 726 cm²