Question

Find the largest volume of a cube that can be enclosed in a sphere of diameter $2cm$

• A. $1c{m}^3$
• B. $2\sqrt{2}c{m}^3$
• C. $\pi c{m}^3$
• D. $\frac{8}{3\sqrt{3}}c{m}^3$

Answer 1

The correct option is D $\frac{8}{3\sqrt{3}}c{m}^3$

Diagonal of cube $=$ Diameter of sphere

$=2$ cm

Let side of cube be '$a$' then

$\Rightarrow 2=\sqrt{a^2+a^2+a^2}\Rightarrow a\sqrt{3}=2\Rightarrow a=\frac{2}{\sqrt{3}}cm$

$\therefore$ Volume of cube $=a^3={\left(\frac{2}{\sqrt{3}}\right)}^3=\frac{8}{3\sqrt{3}}{cm}^3$