Prolate Spheroid Formulas

A prolate spheroid is a surface of revolution obtained by rotating an ellipse about its major axis. Semi-Axes: a, b, b (a>b) Surface Area: S Volume: V $S=2πb(b+{a\ sin^{-1}e)}/e,$ where $e=√{a^2-b^2}/a$ $V=4/3πb^2a$

Ellipsoid Formulas

In geometry, an ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in threeRead More

Spherical Wedge Formulas

In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge’s base). Radius: R Dihedral angle in degrees: x Dihedral angle in radians: α Area of spherical lune: SL Total surface area: S Volume: V $S_L={πR^2}/90\ α=2R^2x$ $S=πR^2+{πR^2}/90\ α=πR^2+2r^2x$ $V={πR^3}/270\ α=2/3R^3x$

Spherical Segment Formulas

In geometry, 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. Radius of sphere: R Radius of bases: r1, r2 Height: h Area of spherical surface:Read More

Spherical Sector Formulas

In geometry, a spherical sector is a portion of a sphere defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. Radius of sphere: RRead More

Spherical Cap Formulas

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 aRead More

Sphere Formulas

A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. Radius: R Diameter: d Surface area: S Volume: V $S=4πR^2$ $V=4/3πR^3H=1/6πd^3=1/3SR$

Frustum of a Right Circular Cone

Frustum of a right circular cone is that portion of right circular cone included between the base and a section parallel to the base not passing through the vertex. Radius of bases: R, r Height: H Slant height: m Scale factor: k Area of bases: S1, S2 Lateral surface area: SL Total surface area: SRead More

Right Circular Cone Formulas

In geometry, a right circular cone is a circular cone whose axis is perpendicular to its base. Radius of base: R Diameter of base: d Height: H Slant height: m Lateral surface area: SL Area of base: SB Total surface area: S Volume: V $H=√{m^2-R^2}$ $S_L=πRm={πmd}/2$ $S_B=πR^2$ $S=S_L+S_B=πR(m+R)=1/2πd(m+d/2)$ $V=1/3S_B\ H=1/3πR^2H$

Right Circular Cylinder with an Oblique Plane Face

Radius of base: R The greatest height of a side: h1 The lowest height of a side: h2 Lateral surface area: SL Area of plane end faces: SB Total surface area: S Volume: V $S_L=πR(h_1+h_2)$ $S=πR^2+πR√{R^2+({h_1-h_2}/2)^2}$ $S=S_L+S_B=πR(h_1+h_2+R+√{R^2+({h_1-h_2}/2)^2})$ $V={πR^2}/2\ (h_1+h_2)$