Spherical segment

In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone.

In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone. ==Measures== If the radius of the sphere is called , the radii of the spherical segment bases are and , and the height of the segment (the distance from one parallel plane to the other) called , then the volume of the spherical segment is V = \frac{\pi}{6} h \left(3 a^2 + 3 b^2 + h^2\right). For the special case of the top plane being tangent to the sphere, we have b = 0 and the solid reduces to a spherical cap. The equation above for volume of the spherical segment can be arranged to V = \biggl [ \pi a^2 \left (\frac{h}{2} \biggr ) \right ] + \biggl [ \pi b^2 \left ( \frac{h}{2} \biggr ) \right ] + \biggl [ \frac{4}{3} \pi \left( \frac{h}{2} \right)^3 \biggr ] Thus, the segment volume equals the sum of three volumes: two right circular cylinders one of radius and the second of radius (both of height h/2 ) and a sphere of radius h/2 . The curved surface area of the spherical zone—which excludes the top and bottom bases—is given by A = 2 \pi R h. Thus the surface area of the segment depends only on the distance between the cutting planes, and not their absolute heights. ==References==

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