Proving the volume of sphere by using tiny volumes

Question

How can I prove the volume of sphere, by using many cones starting at the center of the sphere? It doesn't have to be cones, pyramids also work.

Answer 1

In the formula of the volume in spherical coordinates $$ \int_0^{2\pi}\int_0^\pi\int_0^R\rho^2\sin\phi\,d\rho\,d\phi\,d\theta = \int_0^{2\pi}\int_0^\pi\frac{R^3}3\sin\phi\,d\phi\,d\theta, $$

$$\frac{R^3}3\sin\phi\,d\phi\,d\theta = \frac13(R^2\sin\phi\,d\phi\,d\theta)R$$ can be interpreted as $\frac13$(area of base)(height) of an infinitesimal pyramid.