## [Math] Using cube root in hiking

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.

###### (the post first published at 20240620.)

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