Question

The diagonal of a cube is √6 cm.find the length,area and volume of cube

Answer 1

Answer:

TSA = 12 cm²

LSA = 8 cm²

Volume = 2√2 cm³

Step-by-step explanation:

Let the length of the edge of the cube be a. Then,

Diagonal of a cube = √3a² or a√3

But, given diagonal = √6 cm

∴ a√3 = √6

or, a = √6 ÷ √3 = (√2 × √3) ÷ √3 = √2 cm

Now, we have the length of the edge of the cube as √2 cm.

Thus, Its Total Surface Area = 6 × (√2)² = 6 × 2 = 12 cm²

Lateral Surface Area = 4 × (√2)² = 4 × 2 = 8 cm²

Volume of the cube = (√2)³ = 2√2 cm³