geometry - Surface Area is the derivative of Volume, what is the ...
Aug 4, 2017 · The rate of change of the volume of the sphere is equal to the surface area of the sphere. The outside of the paint is the new boundary of the sphere, and the inside of the paint …
differential geometry - Volume forms and volume of a smooth …
Aug 20, 2015 · 15 Volume is non-unique. Therefore, the smooth structure of a smooth, compact manifold is not enough for the manifold to have a canonical volume. What can happen is, that …
Volume | bartleby
What is the Definition of Volume? Volume is most commonly described as capacity. It is that particular quantity that describes the capacity of an object in free space. In other words, the …
The volume of sphere using integrals - Mathematics Stack Exchange
Aug 11, 2017 · The volume of sphere using integrals Ask Question Asked 8 years, 3 months ago Modified 1 year, 8 months ago
Volume of a Sphere with Cylinder in the Middle
Jan 23, 2021 · If this is the volume of the sphere, I am not sure how I am supposed to show this using the shell method. Any assistance would help! A picture below depicts the problem.
Why does the volume element in spherical polar coordinates …
Oct 11, 2015 · 1 Because the infinitesimal volume element in generic coordinates is generally a prism, so its volume is the magnitude of the vector product of its edge vectors. This can be …
general formula to calculate the volume of any polyhedron
Apr 2, 2025 · With this information, finding the volume is a straight-forward calculation, and one commonly performed. Many analyses of object designs in industry are obtained by …
Volume element in spherical coordinates - Mathematics Stack …
May 7, 2014 · Everything becomes clear if you study analysis on manifolds: you will learn the precise meaning of the volume element and how it behaves under changes of coordinates.
Volume of revolution of polar curve - Mathematics Stack Exchange
May 5, 2017 · The exercise is to derive the formula for the rotation of a polar curve of the form $ r = r ( \\theta ) $ about the $ x $ - axis. When I asked my lecturer, he suggested that I consider a …
integration - Calculate volume of intersection of 2 spheres ...
Dec 5, 2015 · 3) note that the volume that you want is the sum of the volumes of two spherical caps for which you can find the height $h$ and the radius $a$ from the radii of the sphere, the …