# Find the % Volume left when the largest possible sphere is kept in a cube

Dear Student,

When a largest possible sphere kept in a cube , So

Side of cube =  Diameter of sphere  (  As we shoe in following diagram )

Let , Sid e of cube  =  a  , So

Diameter of sphere = a  , Then Radius of sphere  = $\frac{a}{2}$

We know volume of cube =  ( Side )3 , So

Volume of given cube =  a3

And

We know Volume of sphere = , So

Volume of given sphere =

So,

Volume left when the largest possible sphere is kept in a cube =  Volume of cube -  Volume of sphere = a3 -

Therefore,

Percentage of volume left when the largest possible sphere is kept in a cube =

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards

• 0
Hi Prasad, let a be the side of the cube.
Volume of cube = a^3
Now diameter of the sphere will be a