I am only asking for a hint, I do not understand the geometry of the question.
2026-04-08 02:33:45.1775615625
Why is there asymmetry in the metric coefficents of the spherical coordinate system. I am only looking for a hint.
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Let us fix $R$, and look at the sphere of radius $R$. If one fixe $\theta$ (i.e. the latitude), one gets a circle of length $2\pi. R. \sin (\theta)$ (or radius $R \sin(\theta)$. If one fixes t he longitude $\phi$, one gets a great circle of length $2\pi R$.