Question

A cube of side 4cm contain asphere touching its sides .find the volume of the gap in between.

Answer 1

Answer :

The volume of gap in the between is $30.48\:cm^{3}$

Step-by-step explanation :

Given,

Side of cube, a = $4$ cm

Since, it is given that the sphere touches the sides of the cube therefore, the diameter of the sphere will be equivalent to the side of the cube. So, the diameter will be $4$ cm.

Radius of sphere, r = $2$ cm

Now, in order to find the volume of the gap in between, we need to first find the volume of cube and then subtract the volume of sphere from it. So,

Volume of cube -

$\implies(side)^{3}$

$\implies(4)^{3}$

$\implies 64\:cm^{3}$

Volume of sphere -

$\implies\frac{4}{3}\pi r^{3}$

$\implies\frac{4}{3}\times\frac{22}{7}\times 2^{3}$

$\implies 33.52\:cm^{3}$

Volume of gap -

$\implies$ Volume of cube - volume of sphere

$\implies 64-33.52$

$\implies 30.48\:cm^{3}$

Answer 2

Answer -

Volume of cube = $(side)^{3}$

==> $(4)^{3}=64\:cm^{3}$

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

==> $\frac{4}{3}\times\frac{22}{7}\times 2^{3}=33.52\:cm^{3}$

Volume of gap - Volume of cube - volume of sphere

==> $64-33.52=30.48\:cm^{3}$

Note - Here the diameter of the sphere will br equal to side of cube.