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.

Correct result:

a =  4835.9759 m

Solution:

$$\begin{gathered} r=3000\text{ m } \\ V={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 3000^3=113097335529{\text{m}}^3 \\ V=abc=a^3 \\ a=\sqrt[3]{V}=\sqrt[3]{113097335529}=4835.9759\text{ m} \end{gathered}$$

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