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

 

Answers (1)

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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