I've got a hiking backpack, marked as 65 litres.
How to determine its (possible) dimensions?

Calculate \( \sqrt[3]{65} \)

#!/usr/bin/env python3
volume=65 # litres
# as cube
print (volume**(1./3.))

We got ~4. This is a cube with side of 4 decimetres.
Or, if you prefer, 40cm * 40cm * 40cm.

But my backpack is not cubical. It's rather a short bar, maybe.
Find two cubes' dimensions that equals to 65 litres:

\( \sqrt[3]{\frac{65}{2}} \)

#!/usr/bin/env python3
volume=65 # litres
# as two cubes
print ((volume/2)**(1./3.))

We got 3.1 decimeters. That is two cubes with side of 31 cm.
Or, a (short) bar with dimensions: 31cm * 31cm * 31*2 cm.
Or, 31cm * 31cm * 62 cm.

What if my backpack is longer? Like, 3 cubes?

\( \sqrt[3]{\frac{65}{3}} \)

#!/usr/bin/env python3
volume=65 # litres
# as three cubes
print ((volume/3)**(1./3.))

We got ~2.8 decimeters. That is, my backpack may have dimensions 28cm * 28cm * 28*3cm.
Or, 28cm * 28cm * 84cm -- this is close to reality.
(Of course, 28*28*84 = 65856.)

Python has no cube root function, but \( \sqrt[x]{y} = y^{\frac{1}{x}} \) by convention.

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