We can express ratio between the volume of a cube and volume of inscribed sphere in this cube as 6/pi . What is the ratio between these objects when the cube is inscribed in a sphere?

Melina Barber

Melina Barber

Answered question

2022-09-21

We can express ratio between the volume of a cube and volume of inscribed sphere in this cube as 6 / π . What is the ratio between these objects when the cube is inscribed in a sphere?

Answer & Explanation

zmikavtmz

zmikavtmz

Beginner2022-09-22Added 5 answers

Consider the cube within the sphere. It has sides s and long diagonal 2 a, where a is the radius of the sphere. Applying the Pythagorean theorem twice, we can show that s = 2 a / 3 . It then follows that
V s p h e r e V c u b e = 4 3 π a 3 8 a 3 3 3 = 3 π 2 2.7207

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