Discussion
Just one of these four is the reason the polar element carries a factor of the radius. Which?
Answer: A
A wedge of fixed angular width is wider the further out it lies, its arc being \( r\,d\theta \), so a patch far from the origin covers more area than one near it. The factor \( r \) records that. Radians make the arc formula simple but are not the reason, and the behaviour at the origin is a consequence rather than a cause
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