Cube in ball

Cube is inscribed into the sphere of radius 181 dm.

How many percent is the volume of
cube of the volume of the sphere?

Correct result:

p =  36.7553 %

Solution:

r=6 dm D=2⋅ r=2⋅ 6=12 dm  D=3a a=D/3=12/3=4 3 dm≐6.9282 dm  V1=a3=6.92823=192 3 cm3≐332.5538 cm3 V2=43⋅ π⋅ r3=43⋅ 3.1416⋅ 63≐904.7787 dm3  p=100⋅ V1V2=100⋅ 332.5538904.7787≐36.7553  p=2003⋅ π %=36.7553%

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