How to calculate volume of sphere ?

Volume of sphere = $\frac{4}{3} \pi r^3$ r = radius of sphere

How to calculate volume of cube ?

Volume of cube = $a^3$ a = side of cube

GATE (GA) Textile 2022 Question Paper Solution | GATE/2022/GA/02

Question 2 (General Aptitude)

A sphere of radius r cm is packed in a box of cubical shape.
What should be the minimum volume (in cm³) of the box that can enclose the sphere ?

(A)	$\frac{r^3}{8}$
(B)	$r^3$
(C)	$2r^3$
(D)	$8r^3$

[Show Answer]

The description given in the question is drawn in the image above.
Radius of the sphere = r
as the sphere is touching the both sides of cube so the side of side of the cube will be 2r.
Volume of cube = (side of cube)3
= (2r)3
= 8r3

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