Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent the waste was.

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You need to know the following knowledge to solve this word math problem:

algebra
expression of a variable from the formula
solid geometry
cube
sphere
space diagonal
basic functions
percentages
units
volume
8th grade (13y)
9th grade (14y)

We encourage you to watch this tutorial video on this math problem: video1