Consider the following object:
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
If you cut the annulus you get a rectangular ribbon, with length $2\pi\sin\theta$ and height $d\theta$. Its area is then $2\pi\sin\theta d\theta$.