Why is the volume of a sphere $\frac {4} {3}\pi r^3$? 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 was just added
Proofs of the Volume of a Sphere. - Mathematics Stack Exchange 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 seem to find t
Volume of a Sphere with Cylinder in the Middle 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
geometry - Volumes of n-balls: what is so special about n=5 . . . The volume of the simplex also goes to zero, but it falls off slightly faster than the volume of the sphere (1 n! in dimension n vs exp (n) n! for the sphere), since going from 1 to 0 happens faster for $1-y$ than $\sqrt {1-y^2}$