Question

The volume of a cube (in cubic cm) plus three times the total length of its edges (in cms) is equal to twice its surface area (in sq. cm). The length of its diagonal is

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

Answer 1

The correct option is B $6\sqrt{3}$

If the side length of the cube is s inches, then the condition implies
$s^3+3\times 12s=2\times 6s^2$
$\Rightarrow s^3-12s^2+36s=0$
$\Rightarrow s(s^2-12s+36)=0$
$\Rightarrow s{(s-6)}^2=0$
$\therefore s=6$
And the long diagonal has length $=s\sqrt{3}=6\sqrt{3}$