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Geometry and use of trigonometry
  Solid figures
 Pyramid
  A solid whose base is a polygon and whose lateral faces are triangles with a common vertex (apex) is called a pyramid.
A right pyramid is a pyramid in which the line joining the centroid of the base (the point of coincidence of the medians) and the apex is perpendicular to the base.
A regular pyramid is a right pyramid whose base is a regular polygon and lateral faces are congruent isosceles triangles.
The volume of a pyramid is one third of the product of the area of the base and the perpendicular distance from the vertex to the base.
The surface area of a pyramid,      S = B + Slat
The volume of a pyramid,             V = (1/3) · B · h
where,  B is the base area,  Slat  is the lateral surface area and h is the height of the pyramid.
Regular square pyramid

A regular square pyramid has square base and lateral faces are four congruent isosceles triangles making the same angle with the base.

- surface
- volume
Regular triangular pyramid

A regular triangular pyramid has an equilateral triangle base, and three congruent isosceles triangles as lateral faces making the same angle with the base.

R -the radius of the circumcircle,  r -the radius of the incircle
- surface
- volume
 Regular hexagonal pyramid

A regular hexagonal pyramid has a regular hexagon base, and six congruent isosceles triangles as lateral faces making the same angle with the base.

- surface
- volume
 Right pyramidal frustum
B : B1 = (h + x)2 : x2,    where
- surface
P, P1 - bottom and top base perimeter
- volume
 Regular Polyhedrons
 Tetrahedron, octahedron, icosahedron and dodecahedron

The equilateral triangles are faces of, the tetrahedron (4-faced), the octahedron (8) and the icosahedron (20), while the dodecahedron consists of 12 regular pentagons.

Tetrahedron Octahedron
 Solids of revolution

A solid figure generated by revolving a line, curve or a plane figure around a fixed axis is called a solid of revolution.

 Cylinder
A cylinder is solid of revolution generated by rotation of rectangular around one of its sides as the axis of 
revolution.
S = 2B + Slat = 2· r2p  + 2rp · h = 2rp·(r + h)  - surface
V = B ·= r2p · h   - volume
 Cone

A cone is solid of revolution generated by rotation of a right triangle around one of its legs as the axis of revolution.

S = B + Slat = r2p  + rp s = rp (r + s) - surface, V = (1/3) · B ·= 1/3 r2p · - volume
 Conical frustum
 Sphere
A sphere is generated by rotation of a semicircle around its diameter.
S = 4p r2           - surface
V = (4/3)p r3     - volume
 Spherical cap
- surface
- volume
- volume
 Spherical segment
- surface
- volume
 Spherical sector
- surface
- volume
 
 
 
 
 
 
 
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