Recent content by ChemEng92

Of course. I knew it would be a obvious bonehead mistake of mine. Thank you! so much for this and all your help sir.

Good, now I know I am not going crazy looking at this solution haha. Unfortunately there still remains the question of how to obtain the answer he gets. My method was to integrate the differential rectangle: \int_0^{r/a}\int_0^{2\pi} (ad \theta )(a \sin \theta d \phi ) to obtain: -2\pi a^2...

I'm sorry, I'm still not understanding. Here is my issue (maybe in tex it will be clearer, I was learning to use it and this will be my first time): Differential rectangle from diagram: 1. (ad \theta )(a \sin \theta d \phi ) Then he says, "The circle of radius r lies at \theta = r/a." This...

The answer of course makes sense, it is the procedure that is confusing me. Specifically, the step where he goes from deriving the infinitesimal area element (adΘ)(asinΘdΦ) to the part where he says, "Integrating the element of area above...". It is the integrands that make no sense to me. Why...

Hi Chet, Your limits for Θ are correct, IF we are looking to find the area of a hemisphere. However, the calculation I am looking for is the area of a spherical cap, at any angle Θ<π/2 (see attached image in first post). Also, I did the integral you mentioned in your post, however the answer...

r is the radius of the circle inscribed on the sphere, i.e., the distance from the pole of the sphere to the point on the sphere which the circle lies, along a path for which Θ varies but dΦ=0 (definition from the book). I understand of course that area is not negative, but taking the integral...

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...