Find out the ratio of the volume of a cube and volume of a ball, if the ball fits exactly inside the cube

A 2 : π

B π : 6

C 6 : π

D 8 : π

E 9 : π

Correct Answer: Option C

Let the edge of the cube and radius of the ball be x units and r units respectively

As we know, the ball fits exactly inside the cube

∴ Diameter of the ball = Edge of the cube

⇒ 2r = x

Now, Volume of cube = (edge)³ = x³ = 8r³

volume of ball = 4/3 × π r³

⇒ Required ratio \(= \frac{{8{r^3}}}{{\frac{4}{3}\pi {r^3}}} = \frac{6}{\pi }\)

⇒ Required ratio = 6 : π

Hence, the ratio of volumes of the cube and that of the ball is 6 : π