Homework Statement
I've attached the problem, it involves reducing a 3x3 matrix determinant to row echelon form, but the leading diagonal elements have to be linear in a and b afterwards.
Homework Equations
The Attempt at a Solution
I've managed to convert it to row echelon form...
Ah yes, just recognised the problem. I was only imagining r as being the distance to the surface from the z axis, neglecting all the interior volume where it can reduce to 0... Thanks!
Well that is certainly true to get the formula for the volume of the whole sphere, but in this case the minimum value that r takes is \sqrt{R^2-a^2} . Your proposal is one that I have considered, but I don't see how it can be justified.
Homework Statement
A sphere of radius R with centre at the origin is cut by two parallel planes at z=\pm a, where a<R. Write, in cylindrical coordinates, a triple integral which gives the volume of that part of the sphere between the two planes. Evaluate the volume by first performing the r,θ...