A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

Answer : $30.47\; cm^{3}$

Volume of cube is given as $(\text {side length})^{3} = (4\; \text {cm})^{3} = 64 \text {cm}^{3}$

As the cube contains the sphere,

Diameter of sphere = side length of the cube = 4 cm

Radius of sphere $(r)=\frac{4}{2}cm=2cm$

We know that volume of a sphere is given as $\frac{4}{3}\pi r^{3}$                              (where r is the radius)

Volume $=\frac{4}{3}.\frac{22}{7}.2.2.2=\frac{704}{21}cm^{3}$

$\therefore \text {Volume of the gap in between}=\text {Volume of cube}-\text {volume of sphere}$

$=\left ( 64-\frac{704}{21} \right )cm^{3}$

$=\frac{640}{21}cm^{3}$

$=30.47\; cm^{3}$

Hence the required answer is $30.47\; cm^{3}$

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