Question

How many spherical balls of radius 2 cm can be placed inside a cubical box of edge 8 cm?

Answer 1

Volume of box = 8*8*8
volume of balls = 4/3π * 2*2*2
Dividing = (8*8*8)/4/3*3.14*8 = 15
So 15 such balls can be placed in it

Answer 2

Given:

Spherical balls with radius 2 cm. (say $r$)

A cubical box of edge 8 cm. (say $a$)

To Find:

Number of spherical balls that can be placed inside the given cubical box.

Solution:

Since, Volume of a sphere = $\frac{4}{3} \pi r^{3}$

Putting r = 2 cm in it, we get:

Volume of one spherical ball

$= \frac{4}{3} \times \frac{22}{7} \times (2)^{3}\\ \\= \frac{4}{3} \times \frac{22}{7} \times 2 \times 2 \times 2 \\\\= 33.52 \ cm^{3}$

And, also, we know that

Volume of a cube = $a^{3}$

So, putting the value a = 8 cm in it, we get:

Volume of the cubical box = $8 ^{3} = 512 \ cm^{3}$

To find the number of spherical balls that can be placed inside the given cubical box, we will have to divide the volume of the cubical box by the volume occupied by one spherical ball.

Number of spherical balls that can be placed inside the cubical box

                                                                $= \dfrac{Volume \ of \ cubical \ box}{Volume \ of \ one \ spherical \ ball}\\\\= \dfrac{512}{33.52} = 15.27$

15.27 spherical balls can be fitted inside the given cubical box.

OR 15 complete spherical balls can be fitted inside the given cubical box.