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  • A solid ball is exactly fitted inside the cubical box of side a.

Write ‘True’ or ‘False’ and justify your answer in the following : 

A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is \frac{4}{3}\pi a ^{3}

Answers (1)

It is given that the ball is exactly filled inside the cubical box of side a.

           

 Hence the diameter of the sphere = a

\text{ Radius of sphere} =\frac{a}{2}

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

=\frac{4}{3} \pi \left (\frac{a}{2} \right )^{3}

=\frac{4}{3} \pi \times \frac{a^3}{8}

\text{Volume of sphere}=\frac{\pi a ^{3}}{6}

\text{ Hence the volume of the sphere is not equal to }\frac{4}{3}\pi a ^{3}

Hence the given statement is False.

Posted by

infoexpert21

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