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Home » Recall the relationships between spherical and Cartesian coordinates: - Leaselab

Recall the relationships between spherical and Cartesian coordinates: - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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Wait â correction: The correct formula for the circumradius of an eq...
R = rac{s}{\sqrt{3}} \cdot rac{2}{1} \quad ext{(No â accurate for...
Actually, in an equilateral triangle, the circumradius is:
R = rac{s}{\sqrt{3}} \cdot rac{2}{1} \quad ext{Incorrect.}
Correct derivation: The height $ h $ of an equilateral triangle is $ ...
R = rac{2}{3} \cdot rac{\sqrt{3}}{2}s = rac{s}{\sqrt{3}} \cdot rac...
R = rac{s\sqrt{3}}{3}
The area $ A $ of the circular dome is:
A = \pi R^2 = \pi \left( rac{s\sqrt{3}}{3}
ight)^2 = \pi \cdot rac{3s^2}{9} = rac{\pi s^2}{3}

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