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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

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 cap

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 segment

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