Question

a cube rest inside a sphere so that each vertex touches the sphere the radius of the sphere is 6 cm . determine the volume of the cube

Answer 1

`V=432√(2)\ cm^(3)`

Explanation:

we know that

The volume of a cube is equal to

`V=s^(3)`

where s is the length side of a cube

The diagonal of the cube in each face is equal to the diameter of the sphere

so

Applying the Pythagoras theorem

Find the length side s of the cube

`diameter=2*6=12\ cm`

`12^(2) =s^(2)+s^(2)`

`12^(2) =2s^(2)`

`s=6√(2)\ cm`

Find the volume of the cube

`V=(6√(2))^(3)`

`V=432√(2)\ cm^(3)`