# 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:

$r=3000 \ \text{m} \ \\ \ \\ V=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 3000^3=113097335529 \ \text{m}^3 \ \\ \ \\ V=abc=a^3 \ \\ \ \\ a=\sqrt{ V}=\sqrt{ 113097335529 } \doteq 4835.9759 \doteq 4835.976 \ \text{m}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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