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

Answer:

$V=432\sqrt{2}\ cm^{3}$

Step-by-step 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

$diameter=2*6=12\ cm$

$12^{2} =s^{2}+s^{2}$

$12^{2} =2s^{2}$

$s=6\sqrt{2}\ cm$

Find the volume of the cube

$V=(6\sqrt{2})^{3}$

$V=432\sqrt{2}\ cm^{3}$