Question

6. Diagonal of a cube is 6 cm. long. Volume of this cube
(in cm”) will be :​

Answer 1

Answer:

72/root3 cm³

Step-by-step explanation:

Given:

• Diagonal of a cube = 6 cm

To Find:

• What is the volume of cube?

Solution:

☆ Diagonal of cube = (root 3) × side

Hence, side of the cube = Diagonal/root 3

$= \frac{6}{ \sqrt{3} } \: \: cm$

☆ Volume of cube = (side)³

$({ \frac{6}{ \sqrt{3} } )}^{3} \\ = \frac{6 \times 6 \times 6}{ \sqrt{3} \times \sqrt{3} \times \sqrt{3} } \\ = \frac{216}{\sqrt{27} } \\ = \frac{216}{3 \sqrt{3} } \\ \: \: \: \: \: \: \: \: = \frac{72}{ \sqrt{3} } \: {cm}^{3}$

Therefore, Volume of cube = 72/root3 cm³.