Your derivation is very interesting! I hope someday I can get to this level of derivation- I've only just completed the BC track and will be entering multivariable calc next semester.
Thank you for you help, on both forums!
I'm actually working on this as we speak, and realized, of course, that my formula was not correct. However, I decided to go back to spherical sectors.
If you look at the 1st image http://mathworld.wolfram.com/SphericalSector.html" , imagine that the initial line was the line going directly...
Hello,
I've just found a book which mentions the formula for calculating the volume of a rotated polar function:
\int_{\theta_1}^{\theta_2} \frac{2}{3} \pi r^3 sin(\theta) d\theta
How does one calculate this? In an https://www.physicsforums.com/showthread.php?t=457896", I calculated that the...
Hello again,
I forget to say that the integral I mention above does not calculate the correct volume e.g. for a circle r=1. It gives a volume of 2pi, when it should be 4/3 pi.
Thanks again for any help you can offer!
Hello,
I was wondering if anyone could help me with deriving the volume created by the rotation of a polar equation around the initial line.
So, I thought about adding the surface area of cones (multiplied by d\theta) if each cone the triangle created with s-length of f(\theta) and r-length...