Question

The cube has volume $64$ cubic units. If a largest sphere possible that can be placed inside this cube has radius $r$, then the value of $r$ is

• A. $2$
• B. $2\sqrt{2}$
• C. $4$
• D. $8$

Answer 1

The correct option is A $2$

Since we have to fit the sphere with maximum volume inside a cube and because the cube is uniform in all the three directions, so as the sphere, we just need to fit the diameter of the sphere in one side of the cube.

Since the volume of the cube is $64$ cubic units, its side is $4$ units.

Therefore, the maximum diameter of the sphere would be $4$ units and thus the radius becomes of $2$ units.