GATE CH 2022 | GA Question: 2

Question

A sphere of radius $r$ $\text{cm}$ is packed in a box of cubical shape.

What should be the minimum volume (in $\text{cm}^{3}$) of the box that can enclose the sphere?

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

Answer 1

Let the side of a cube be $a\;\text{cm}.$

The diameter of a sphere is equal to the side of a cube.

$\Rightarrow \boxed{a = 2r}$

$\therefore$ The volume of a box of the cubical shape $ = a^{3} = (2r)^{3} = 8r^{3} \;\text{cm}^{3}.$

Correct Answer $:\text{D}$