Question

A sphere is inscribed in a cubical box such that the sphere is tangent to all six faces of the box, What is the ratio of the volume of the cubical box to the volume of sphere?

• A. $6\pi$
• B. $36\pi$
• C. $\frac{4\pi }{3}$
• D. $\frac{6}{\pi }$

Answer 1

The correct option is D $\frac{6}{\pi }$

Front View:
Diameter of sphere $=$ side of cube $=a$
We know $r=\frac{a}{2}$
$\frac{V\left(\text{cube}\right)}{V\left(\text{sphere}\right)}=\frac{a^3}{\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^3}=\frac{24a^3}{4\pi a^3}=\frac{6}{\pi }$