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:

$r=3000 \ \text{m} \ \\ \ \\ V=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 3000^3=113097335529 \ \text{m}^3 \ \\ \ \\ V=abc=a^3 \ \\ \ \\ a=\sqrt[3]{ V}=\sqrt[3]{ 113097335529 } \doteq 4835.9759 \doteq 4835.976 \ \text{m}$

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