Question

A sphere of radius $r$ lies inside a cube and touches each of the six sides of the cube. Calculate the volume of the cube in terms of $r$.

• A. $r^3$
• B. $2r^3$
• C. $4r^3$
• D. $\frac{4}{3}\pi r^3$
• E. $8r^3$

Answer 1

The correct option is E $8r^3$

The side of the cube is the diameter of the sphere i.e. $2r$.
Volume of cube $={\left(2r\right)}^3={8r}^3$.