Volumes and areas of body surfaces Volumes and areas of body surfaces: prism, parallelepiped, right prism, right-angled parallelepiped, cube, pyramid, regular pyramid, truncated pyramid, regular truncated pyramid, circular cylinder, round cylinder, circular cone, round cone, truncated circular cone, truncated round cone, sphere (ball), hemisphere, spherical segment, spherical layer, spherical sector, hollow ball. Designations: V – […]

## Similarity of bodies

Similarity of bodies Similar bodies. Mirror similar bodies. Relations of corresponding sizes in similar figures and bodies. Two bodies are similar, if one of them can be received from another by increasing (or decreasing) of all its linear dimensions by the same ratio. A car and its model are similar bodies. Two bodies (or figures) […]

## Symmetry. Symmetry of plane figures

Symmetry. Symmetry of plane figures Mirror symmetry. Symmetry plane. Symmetrical figures. Mirror equal figures. Central symmetry. Symmetry center. Rotation symmetry. Symmetry axis. Axial symmetry. Examples of a symmetry kinds. Symmetry of plane figures. Examples of symmetry of plane figures. Mirror symmetry. A geometric figure is called a symmetrical relatively a plane S ( Fig.104 ), […]

## Regular polyhedrons

Regular polyhedrons Regular polygons. Convex regular polyhedrons: tetrahedron, hexahedron (cube), octahedron, dodecahedron, icosahedron. Non-convex regular polyhedrons. A polyhedron is called a regular one, if all its faces are equal regular polygons and the same number of faces join in each its vertex. It is known only five convex regular polyhedrons and four non-convex regular polyhedrons. […]

## Solid angles

Solid angles Solid angle. Measure of a solid angle. Steradian. A solid angle is a part of a space, concluded inside of one part of a conic surface with a closed directrix. A solid angle is measured by a piece of spherical surface ( ABCDEF, Fig.98 ). A measure of a solid angle is a […]

## Tangent plane of a ball, a cylinder and a cone

Tangent plane of a ball, a cylinder and a cone Tangent planes of curved surfaces: spherical surface, surface of a round cylinder, surface of a round cone. Cylinder inscribed into a prism. Cylinder circumscribed around a prism. Cone inscribed into a pyramid. Cone circumscribed around a pyramid. Consider three points A, B, C on a […]

## Ball (sphere)

Ball (sphere) Spherical surface. Ball (sphere). Center, radius and diameter of a ball. Sections of a ball. Large circle. Archimedean theorem. Parts of a ball: spherical segment, spherical layer, spherical zone, spherical sector. Spherical surface is a geometrical locus in a space, that is a totality of all points, equally removed from one point O, […]

## Cone

Cone Conic surface. Directrix, generatrices and vertex of a conic surface. Cone. Pyramid as a particular case of a cone. Circular cone. Axis of a cone. Round cone. Conic sections. Conic surface is a surface, formed by a motion of a straight line ( AB, Fig.85 ), which goes constantly through an immovable point ( […]

## Cylinder

Cylinder Cylindrical surface. Directrix and generatrices of a cylindrical surface. Cylinder. Right cylinder. Oblique cylinder. Circular cylinder. Round cylinder. Prism as a particular case of a cylinder. Cylindrical sections. Cylindrical surface is a surface, formed by a motion of a straight line (AB, Fig.82 ), which saves the same direction and intersects with the given […]

## Polyhedrons. Prism, parallelepiped, pyramid

Polyhedrons. Prism, parallelepiped, pyramid Polyhedron. Convex polyhedron. Prism. Right prism. Oblique prism. Regular prism. Normal (orthogonal) section of a prism. Parallelepiped. Right parallelepiped. Right-angled parallelepiped. Cube. Pyramid. Regular pyramid. Truncated pyramid. Regular truncated pyramid. Polyhedron is a body, boundary of which consists of pieces of planes (polygons). These polygons are called faces, their sides – […]