Question

The total surface area of cube is $100c{m}^3$. Find its volume.

• A. ${\left(\frac{100}{6}\right)}^{\frac{2}{3}}$
• B. ${\left(\frac{100}{6}\right)}^{\frac{1}{2}}$
• C. ${\left(\frac{100}{6}\right)}^{\frac{3}{2}}$
• D. None

Answer 1

The correct option is C ${\left(\frac{100}{6}\right)}^{\frac{3}{2}}$

Let the length of side of cube $=l$ cm.

Then, Total surface area of cube$=6l^2$.

Given, the total surface area of the cube $=100c{m}^3$.

$⟹100=6l^2$

$⟹l^2=\frac{100}{6}$

$⟹l={\left(\frac{100}{6}\right)}^{\frac{1}{2}}$.

Then, Volume of cube $V=l^3={\left[{\left(\frac{100}{6}\right)}^{\frac{1}{2}}\right]}^3$

$\therefore$ Volume of cube $={\left(\frac{100}{6}\right)}^{\frac{3}{2}}$.

Hence, option $C$ is correct.