A solid ball is exactly fitted inside the cubical box of side `a`. The volume of the ball is .

Options

A. `(1)/(3) pia^(3)`
B. `(4)/(3) pia^(3)`
C. `(1)/(6) pia^(3)`
D. can not be determined

Answer

C

Explanation

False
Because solid ball is exctly fitted inside the cubical box of side a. So, os the diameter for the solid ball.
`therefore`" " Radius of the ball `= (a)/(2)`
So, " " volume of the ball `= (4)/(3) pi ((a)/(2))^(3) = (1)/(6) pia^(3)`