May 20, 2022 · Now if I have a sphere of radius r, and I increase the radius by a tiny amount, dr, then the new, expanded sphere has a volume that is bigger, by the volume of the thin spherical shell that …

Sep 2, 2020 · 2 I was asked to explain why the volume of a sphere is $\frac {4} {3}\pi r^3$ to a student that does not have the knowledge of calculus. In doing so I thought of an argument and I cannot …

Dec 6, 2024 · The sphere has the minimum surface to volume ratio for solids of a given fixed volume. In your calculation the volumes of the cube and the sphere with the particular surface to volume ratio …

May 11, 2013 · I want a simple proof for the formula of volume of sphere. Does the proof/explanation without integration possible?

Dec 8, 2015 · Rate of Change of Volume in a Sphere Ask Question Asked 10 years ago Modified 6 years, 7 months ago

Aug 11, 2017 · The volume of sphere using integrals Ask Question Asked 8 years, 4 months ago Modified 1 year, 9 months ago

You can see that not all such cylinders have equal volume, just by considering the extreme case of when two of the points are very close together. You get either a long thin rod, or a big flat pancake, …

Jun 8, 2019 · A sphere is a 3-dimensional object. The 2-dimensional analogue of a sphere is a circle.

Find the volume of a "cap" of the yellow sphere (centered at the origin) above the blue plane. Multiply that volume by 2.0 due to symmetry, for the cap of the red sphere below the blue plane.

May 16, 2015 · How proof that $\omega$ is the volume form? The first thing that comes to mind is show that $\int_ {S^ {n-1}}\omega=Vol (S^ {n-1})$ but I have serious problems with the definition, I think …