Question

Surface area and volume of a cubic section using spherical coordinates:

Answer 1

A section of a sphere is defined with:
\[0 \le r \le 2\]
\[0 \le \theta \le 90^{o}\]
\[30^{o} \le \phi \le 90^{o}\]

I need the area and volume of the area described.

Answer 2

The SA should be around 4.188 and the Volume is 2.79 from using just the formulas.

Answer 3

I have set up the integrals a dozen times and cant get those numbers.

Volume should be something like this, correct?
\[\int\limits_{30}^{90}\int\limits_{0}^{90}\int\limits_{0}^{2} R ^{2}\sin \theta d \theta d \phi\]

Answer 4

And surface area this: \[\int\limits_{0}^{90}\int\limits_{30}^{90} R ^{2} \sin \theta d \theta \]

Answer 5

@phi - I already owe you a lunch for the last time you helped me out, any chance for an opinion on this one?

Answer 6

nm I got it :)