Area of a ring

1. Oct 22, 2015

Calpalned

How was the equation for area of a ring derived?

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2. Oct 22, 2015

Calpalned

I can derive the area as the difference of the areas of two circles. $= \pi(R+dR)^2 - \pi R^2$
But I don't think this $\pi (R+dR)^2 - \pi R^2$ is equal to $(2/pi R)(dR)$ given in the beginning.

3. Oct 22, 2015

PeroK

No, but it's an approximation for small $dR$.

4. Oct 22, 2015

mathman

When setting up integrals, the differential is assumed to be vanishing small, so that terms proportional to the powers of the differential can be neglected.