Formula

The lateral area A of a spherical cap of radius r and height h is given by: A = [latex]2πrh [/latex]. The volume V of a spherical segment is obtained by using the formula : V = [latex]\dfrac{πh(3q^{2} + h^{2})}{6}[/latex] where [latex]h[/latex] is the height of the segment and [latex]q[/latex] is the radius of the small circle. The Pythagorean theorem can be applied to the right triangle shown in the figure above, in which [latex]\left ( R-h \right )^{2}+r^{2}=R^{2}[/latex], to deduce that [latex]r^{2}=2Rh-h^{2}[/latex], where the radius [latex]r[/latex] of the spherical segment has a value of [latex]\sqrt{h(2R-h)}[/latex].The preceding formula to calculate the volume of a spherical segment as a function of the height [latex]h[/latex] and the radius [latex]R[/latex] of the sphere becomes: [latex]V = \dfrac{\pi h^2 (3r-h)}{3}[/latex].