Question

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

• A. $\frac{125\sqrt{3}}{72}$
• B. $\frac{625}{8}$
• C. $\frac{125\sqrt{2}}{32}$
• D. $\frac{128}{8}$

Answer 1

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

Diagonal of cube $\left(d\right)=\sqrt{3}.a$

$\therefore volumeofcube=a^3=\frac{d^3}{(\sqrt{3}{)}^3}=\frac{{\left(2.5\right)}^3}{3\sqrt{3}}=\frac{125\sqrt{3}}{72}$