Alien ship

The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the largest possible volume.

Result

a =  4835.976 m

Solution:

r=3000 m  V=43⋅ π⋅ r3=43⋅ 3.1416⋅ 30003=113097335529 m3  V=abc=a3  a=V3=1130973355293≐4835.9759=4835.976  m r = 3000 \ m \ \\ \ \\ V = \dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3 = \dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 3000^3 = 113097335529 \ m^3 \ \\ \ \\ V = abc = a^3 \ \\ \ \\ a = \sqrt[3]{ V} = \sqrt[3]{ 113097335529 } \doteq 4835.9759 = 4835.976 \ \text { m }

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