A solid spherical cap of radius R is the solid delimited by a sphere of radius R and a plane

that intersects the sphere. The height h of the solid spherical cap is the largest distance from a point of the solid to the plane intersecting the sphere. Show that the volume of a solid spherical cap is πh^2(3R-h)/3. It is enough to consider the solid spherical cap delimited by the sphere x^2 +y^2 + z^2 = R^2 and the plane z= R-h