Spherical Cap Calculation
Calculators and formulas for volume and surface area of a spherical cap
This function calculates the volume and surface area of a spherical cap. A spherical cap or spherical dome is a portion of a sphere cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane.
To perform the calculation, enter the spherical radius and the height or radius of the cap. Then press the 'Calculate' button.
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Formulas for the spherical segment
Cap volume (\(\small{V_s}\))
\(\displaystyle V_s=\frac{1}{3}·π·h^2·(3·r - h)\)
Cap height (\(\small{h}\))
\(\displaystyle h=r-\sqrt{r^2 -a^2}\)
Cap radius (\(\small{a}\))
\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)
Cap surface area (\(\small{S_C}\))
\(\displaystyle S_C=2·π·r·h\)
Cap base area (\(\small{A}\))
\(\displaystyle A=a^2 ·π\)
Cap surface (\(\small{S}\))
\(\displaystyle S=S_C+A\)
Sphere radius (\(\small{r}\))
\(\displaystyle r=\frac{S_c}{2·π·h}\)
Round solids functions
Sphere • Spherical cap • Spherical sector • Spherical segment • Spherical ring • Spherical wedge • Spherical corner • Spheroid • Triaxial ellipsoid • Ellipsoid volume • Spherical shell • Solid angles • Torus • Spindle torus • Oloid • Elliptic Paraboloid
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