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Spherical cap and spherical segment

This calculator computes volume and surface area of spherical cap and spherical segment
Anton2011-07-16 07:23:47

Spherical cap Spherical cap

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere.

Formulae:
S_{lateral}=2 \pi R H - lateral surface area
S_{base}=\pi{H}(2R-H) - base surface area
V=\pi H^2(R- \frac{1} {3} H) - volume

Spherical capCreative Commons Attribution/Share-Alike License 3.0 (Unported)
0.12345678901234567890
 
 
 
 



spherical segment

spherical segment

A spherical segment is the solid defined by cutting a sphere 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.

Formulae:
S_{lateral}=2 \pi R (H_2-H_1) - lateral surface area
V = \pi \left[ H_2^2 \left( R - \frac{1} {3} H_2 \right) - H_1^2 \left( R - \frac{1} {3} H_1 \right) \right] - volume

Spherical segmentCreative Commons Attribution/Share-Alike License 3.0 (Unported)
0.12345678901234567890
 
 
 

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