Question

The largest volume of a cube that can be enclosed in a sphere of diameter $2cm$ is (in ${cm}^3$)

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

Answer 1

Answer: (B)

$2\sqrt{2}$

The largest cube that can be enclosed in a sphere will have its diagonal equal to the diameter of the sphere.
Hence, length of the diagonal of the cube of side $a$ is $\sqrt{3}a=2cm$

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

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