Spherical Cap Formulas

Posted In: Mathematics

In geometry, a spherical cap, spherical dome, or spherical segment of one base is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere.

Spherical Cap

Radius of sphere: R
Radius of base: r
Height: h
Area of plane face: SB
Area of spherical cap: SC
Total surface area: S
Volume: V

  1. $R={r^2+h^2}/{2h}$
  2. $S_B=πr^2$
  3. $S_C=π(h^2+r^2)$
  4. $S=S_B+S_C=π(h^2+2r^2)=π(2Rh+r^2)$
  5. $V=π/6h^2(3R-h)=π/6h(3r^2+h^2)$

Post Tags: Geometry

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