使用极限法推导球缺面积和体积公式

he derivation of the spherical cap area and volume formulas is often obtained by calculus or other indirect methods in the previous literature, but this paper proposes a method to directly derive the area and volume formulas of the spherical cap by applying the limit idea only using elementary mathematics knowledge. The simplification methods of trigonometric function and chart elimination in the derivation process have certain general reference, and the simplest formulas of side surface area and volume of spherical inscribed multi-layer stacked conical frustum derived in the intermediate process can also be directly applied when discrete summation is required. In addition, the case of using cylindrical approximation is also discussed.