volume of a spherical sector of a 4-sphere How does one calculate the volume of a spherical sector of a 4-sphere?
In 3-dimensions, this is $V=\frac{2 \pi r^2 h}{3}$, where $h$ denotes the height of the cap.

This paper

Li, Shengqiao. "Concise formulas for the area and volume of a hyperspherical cap." Asian Journal of Mathematics and Statistics 4.1 (2011): 66-70.
  Journal link.

reaches an equation for the volume of a hyperspherical cap in $\mathbb{R}^2$:

          


See the paper to interpret the notation.
