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Consider the following object:

enter image description here

I want to calculate the area of the annulus. The annulus is within the region of $$ \theta $$ and $$ \theta + d\theta $$

The answer of the area of the annulus is apparently $$ 2\pi sin(\theta)d\theta $$ but I am unsure why this is. Any explanation would be useful

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  • $\begingroup$ Spherical coordinates are the way to go. Once you understand the definition you will be able to set up the integral and evaluate it quickly. $\endgroup$ – Charlie Frohman Feb 18 at 12:20
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If you cut the annulus you get a rectangular ribbon, with length $2\pi\sin\theta$ and height $d\theta$. Its area is then $2\pi\sin\theta d\theta$.

enter image description here

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