Question

The length of the diagonal of a cube is `6sqrt(3)` cm. Its total surface area is ______.  

Options

• 144 cm²

•  216 cm²

• 180 cm²

• 108 cm²

Answer 1

The length of the diagonal of a cube is `6sqrt(3)` cm. Its total surface area is 216 cm².

Explanation:

Let the edge of the cube be a cm.

Then, length of the diagonal `=sqrt(3"a")`

or,

`sqrt(3"a") = 6sqrt(3)`

⇒ a = 6 cm 

Therefore, the total surface area of the cube = 6a² 

`= (6xx6xx6) "cm"^3`

= 216 cm³  

Therefore, the total surface area of the cube = 6a² 

= (6 × 6 × 6 ) cm³ 

= 216 cm³