Posts for Tag: Geometry

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 $S_L=πR(h_1+h_2)$ $S=πR^2+πR√{R^2+({h_1-h_2}/2)^2}$ $S=S_L+S_B=πR(h_1+h_2+R+√{R^2+({h_1-h_2}/2)^2})$ $V={πR^2}/2\ (h_1+h_2)$

Right Circular Cylinder

A right circular cylinder is a cylinder whose base is a circle and whose elements are perpendicular to its base. Radius of base: R Diameter of base: d Height: H Lateral surface area: SL Area of base: SB Total surface area: S Volume: V $S_L=2πRH$ $S=S_L+2S_B=2πR(H+R)=πd(H+d/2)$ $V=S_B\ H=πR^2H$

Dodecahedron Formulas

In geometry, a dodecahedron (plural: dodecahedra) is a polyhedron with twelve flat faces, twenty vertices and thirty edges. The term is most commonly used to refer to the regular dodecahedron, a Platonic solid composed of twelve equilateral pentagon. Edge: a Radius of inscribed circle: r Radius of circumscribed circle: R Surface area: S Volume: VRead More

Icosahedron Formulas

In geometry, an icosahedron (plural: icosahedra) is a polyhedron with twenty faces, thirty edges, and twelve vertices. The term is most commonly used to refer to the regular icosahedron, a Platonic solid composed of twenty equivalent equilateral triangles, four of which meet at each vertex. Edge: a Radius of inscribed circle: r Radius of circumscribedRead More

Octahedron Formulas

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Edge: a Radius of inscribed circle: r Radius of circumscribed circle:Read More

Rectangular Right Wedge

Sides of base: a,b Top edge: c Height: h Lateral surface area: SL Area of base: SB Total surface area: S Volume: V $S_L=1/2(a+c)√{4h^2+b^2}+b√{h^2+(a-c)^2}$ $S_B=ab$ $S=S_b+S_L$ $V={bh}/6(2a+c)$

Frustum of a Regular Pyramid

The Frustum of a regular pyramid is the result of chopping the top off a regular pyramid. It is also called truncated pyramid. Base and top side lengths: $\{\table a_1,a_2,a_3,…,a_n;b_1,b_2,b_3,…,b_n$ Height: h Slant height: m Mi,ber of sides: n Area of bases: S1,S2 Lateral surface area: SL Perimeter of bases: P1,P2 Scale factor Total surfaceRead More

Regular Pyramid Formulas

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length. Side of base: a Lateral edge: b Height: h Slant height: m Mi,ber of sides: n Semiperimeter of base: p Radius of inscribed sphere of base: r Area of base: SB Lateral surface area:Read More