The volume of a straight cone in $\mathbb R^3$ is usually find adding the circular sections orthogonal to the height. If the base has radius $R$ and the height is $h$ we have: $$ V_{C3}=\int_0^h \pi r^2 dz=\pi \int_0^h \frac{R^2}{h^2}z^2 dz=\pi \frac{R^2}{h^2} \frac{1}{3} h^3= \frac{1}{3}\pi R^2 ...