Question

Write True or False and justify your answer in the following.

A solid ball is exactly fitted inside the cubical box of side b, The volume of ball is `4/3 πb^3`.

Answer 1

This statement is false.

Explanation:

If the sphere is exactly fitted inside the cube of side b then its diameter = b, so `r = b/2`. 

The sphere volume is `V = 4/3 πr^3`. 

So, `V = 4/3 π(b/2)^3` 

= `4/3 π(b^3/8)`

= `4/24 πb^3`

= `1/6 πb^3` 

Thus, the correct volume is `1/6 πb^3`, not `4/3 πb^3`. 

The sphere volume formula used above is `V = 4/3 πr^3`.