Question

Kamal says “If a solid ball is exactly fitted in a cubical box of side ‘a’ units. Then the

volume of the ball is 4 /3a^3

a cubic units. Do you agree with him?. Give reason.​

Answer 1

NO, I don't agree with Kamal.

• If the length of side of cubical box is 'a' units, then a sphere of diameter a units could fit into it.
• This implies that the radius of the sphere would be 'a/2' units.
• The volume of a sphere with radius "a/2" units will be  $\frac{4}{3}\pi (\frac{a}{2} )^{3}$.
• Therefore the volume of the ball that can exactly fit into the cubical box will be $\frac{\pi (a^{3}) }{6}$.
• Therefore Kamal is incorrect.