Inscribed sphere

How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?

Result

p =  52.36 %

Solution:

a=6 r=a/2=6/2=3 V1=4/3π r3=4/3 3.1416 33113.0973 V2=a3=63=216 p=100 V1/V2=100 113.0973/21652.359952.36a=6 \ \\ r=a/2=6/2=3 \ \\ V_{ 1 }=4/3 \pi \cdot \ r^3=4/3 \cdot \ 3.1416 \cdot \ 3^3 \doteq 113.0973 \ \\ V_{ 2 }=a^3=6^3=216 \ \\ p=100 \cdot \ V_{ 1 }/V_{ 2 }=100 \cdot \ 113.0973/216 \doteq 52.3599 \doteq 52.36 \\%



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