Question

The volume of a sphere is $\frac{4}{3}\pi r^{3}cucm$. What is the ratio of the volume of a cube to that of a sphere which will fit inside the cube ?

• A. $4:3\pi$
• B. $2:\pi$
• C. $8:\pi$
• D. $6:\pi$

Answer 1

The correct option is D $6:\pi$

The sphere fits in the cube. Hence, the edge of the cube will be $2r$.
Volume of cube $=(2r{)}^3=8r^3$
$\therefore$ Ratio of the volume of cube to that of a sphere $=\frac{8r^3}{\frac{4}{3}\pi r^3}=\frac{6}{\pi }$