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 answer:

a =  4835.9759 m

Step-by-step explanation:

$$\begin{gathered} r=3000\text{m} \\ V=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 3000^3=113097335529.23{\text{m}}^3 \\ V=abc=a^3 \\ a=\sqrt[3]{V}=\sqrt[3]{113097335529.23}=4835.9759\text{m} \end{gathered}$$

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