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Volume of a Partially Cut Spherical Cap

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Calculates the volume and surface area of a partially cut spherical cap.
Radius of the base of the segmented solid of revolution: a
Height of the circular segment h
Distance to the cross-section: d
(-a<=d<=a)
Radius of the circle containing the segment r 
Volume V 
Surface area of the spherical portion Ss 
Lateral area of the cross-section Sc 
Base area Sb 
Total Surface Area S (=Ss + Sc + Sb) 
\(\normalsize Partial\ spherical\ cap\\ (1)\ radius:\hspace{10px} r={\large\frac{a^2+h^2}{2h}}\\ (2)\ volume:\hspace{10px} V={ \large\int_{\small -a}^{\small d} S(x) dx } \\ (3)\ surface:\hspace{10px}S={ \large\int r(x)\theta (x) ds } \\\)

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