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1. Homework Statement
Hi all, I am working through Gravity by James Hartle and have become stuck on a question asking me to calculate the area of a circle of radius r in the 2D geometry that is the surface of a sphere of radius a.
A surface element on this sphere can be found to be (adΘ)(asinΘdΦ) (see attached image).
Homework Equations
The Attempt at a Solution
Integrating the above surface element over Θ=0 to Θ=r/a, and Φ=0 to Φ=2π, I obtain A=2πa^{2}cos(r/a). The answer given in the solutions manual is this, plus 2πa^{2}. I don't understand how the additional 2πa^{2} comes about.
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