The diagonal of a cube is 6 square root of 3 cm.

Question

Find the lateral area, surface area, and volume of the cube.? 

Answer 1

Let "a" be the side of the cube.

Find the diagonal AB:

Using pythogoras theorem, we can find DB

DB² = DC² + CB² = a² + a² = 2a²

Now, find the diagonal AB Using pythogoras theorem

AB² = AD² + DB² = a² + 2a² = 3a²

AB = √3a

 

                           

Now find the side lenth of the cube

AB =(v3)a = 6 √ (3)

a = 6

Side length of cube = 6cm

1. Lateral area = 4a² = 4 * 6² = 144 cm²

2. Surface Area = 6a² = 6 * 6² = 216 cm²

3. Volume = a³ = 6³ = 216 cm³