Find Length Of Rolled Up Material Without Unrolling (Applied Calculus Problem and Solution )

[@PhilEdwardsInc]

Wow, this is so cool and I can imagine a lot of interesting applications!

[@VAM_Physics_and_Engineering]

Thanks Phil

[@WonderOfNature1234]

Very important video !

[@scienceandengineering1432]

Such a smooth joke at the beginning.

[@zacs2118]

Can’t you just:
Circumference of inner layer: i
Circumference of outer layer: o
Average circumference (middle layer): a
Total length: t
Number of layers = 3
i + o / 2 = a
a x 3 = t
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Let’s say that we have a rolled up material with 3 layers, the innermost layer has a diameter of 1cm, and the outermost layer a diameter of 3cm. We know that the total length of the roll measured is 18,84cm ☑️.
1 x π Layer 1 C = 3,14 cm
2 x π Layer 2 C = 6,28 cm ⬅️
3 x π Layer 3 C = 9,42 cm
3,14 + 9,42 / 2 = 6,28 ⬅️
6,28 x 3 = 18,84 ☑️