Posts for Tag: Geometry

Conics Formulas – HSC Math

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse. Identification of conics from general formula: $ax^2+by^2+2gx+2fy+2hxy+c=0$ $i. ab-h^2=0, Parabola$ $ii. ab-h^2>0, Ellipse$ $ii. ab-h^2<0, Hyperbola$ $iv.Read More

Circular Torus Formulas

Major radius: R Minor radius: r Surface area: S Volume: V $S=4π^2Rr$ $V=2π^2Rr^2$

Oblate Spheroid Formulas

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

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 $S=4πR^2$ $V=4/3πR^3H=1/6πd^3=1/3SR$