Question

In a cube if the length of diagonal is $\sqrt{12}cm$ cm, then the volume of the cube is

• A. $8\sqrt{12}c{m}^3$
• B. $8c{m}^3$
• C. $16\sqrt{2}c{m}^3$
• D. $16c{m}^3$

Answer 1

The correct option is B $8c{m}^3$

Let ‘a’ be side cube.
Since length of diagonal = $\sqrt{12}$ cm
$\therefore \sqrt{a^2+a^2+a^2}=\sqrt{12}$
Squaring both sides,
$3a^2=12or{a}^2=4ora=2$
Volume of cube $=2\times 2\times 2=8c{m}^3$