Question

If the length of the diagonal of a cube is $6\sqrt{3}$ cm, then the length of the edge of the cube is

• A. $2$ cm
• B. $6$ cm
• C. $3\sqrt{2}$ cm
• D. $4$ cm

Answer 1

Answer: (B)

$6$ cm

Length of the diagonal of a Cuboid = $\sqrt{(l^2+b^2+h^2)}$.

For a cube, $l=b=h$

So, $D=\sqrt{(l^2+l^2+l^2)}=l\sqrt{(}3)$

Length of the diagonal $=6\sqrt{3}$ cm

We need to find edge of cube.

$D=\sqrt{3}l$
$\Rightarrow \sqrt{3}l=6\sqrt{3}$

$\Rightarrow l=6$
Therefore, edge $=$ $6$ cm