Question

The volume (in $m^3$) of cube whose diagonal is $2.5$ meter is:

• A. $\frac{125\sqrt{3}}{72}$
• B. $\frac{625}{8}$
• C. $\frac{125\sqrt{2}}{32}$
• D. $\frac{125}{8}$

Answer 1

The correct option is A $\frac{125\sqrt{3}}{72}$

The diagonal of a cube is given by $a\sqrt{3}=2.5$

$\therefore a=\frac{2.5}{\sqrt{3}}=\frac{2.5\sqrt{3}}{3}$

Volume of the cube is given by $a^3={\left(\frac{2.5\sqrt{3}}{3}\right)}^3=\frac{125\sqrt{3}}{72}$ cu m.