Surface area of ​​a regular octagonal prism. Regular octagonal prism

More meanings of this word and English-Russian, Russian-English translations for OCTAGONAL PRISM in dictionaries.

  • PRISM - f. prism
    Russian-English Dictionary of the Mathematical Sciences
  • PRISM - Prism
    Russian-American English Dictionary
  • PRISM - prism through a prism (rd.) - in the light (of)
    English-Russian-English dictionary of general vocabulary - Collection of the best dictionaries
  • PRISM
    Russian-English dictionary of general topics
  • PRISM - prism
    Russian Learner's Dictionary
  • PRISMA - w. prism through the prism (rd.) - in the light (of)
    Russian-English dictionary
  • PRISMA - w. prism ♢ through the prism (rd.) – in the light (of)
    Russian-English Smirnitsky abbreviations dictionary
  • PRISM - V block, prism, V
    Russian-English dictionary of mechanical engineering and production automation
  • PRISMA - husband. prism .. - through a prism
    Russian-English short dictionary of general vocabulary
  • PRISM - prism, (in foundation calculations) wedge
    Russian-English dictionary on construction and new construction technologies
  • PRISM - Prism
    British Russian-English Dictionary
  • PRISM - prism; through ~y (rd.) in the light (of); ~atic prismatic
    Russian-English Dictionary - QD
  • PRISMA - husband. prism through the prism of prism|a - g. prism through ~y (rd.) in the light (of) ~atic prismatic
  • PRISMA - prism prism
    Russian-English Dictionary Socrates
  • OCTAGONAL CUTTING PLATE - octagonal insert
    Modern Russian-English dictionary of mechanical engineering and production automation
  • OCTAGONAL STAR - lat. stella octangula
    Large Russian-English Dictionary
  • STELLA OCTANGULA
  • SLIDING TRIANGLE - sliding prism; collapse prism
    Large English-Russian Dictionary
  • RUBBLE TOE - stone persistent prism; stone drainage prism
    Large English-Russian Dictionary
  • ROCKFILL TOE - rockfill thrust prism; rockfill drainage prism
    Large English-Russian Dictionary
  • PRISM - noun prism prism prism prism
    Large English-Russian Dictionary
  • OCTAGONAL PRISM - mat. octagonal prism
    Large English-Russian Dictionary
  • OBLIQUE PRISM - oblique prism, oblique prism
    Large English-Russian Dictionary
  • KNIFE EDGE - 1. support prism 2. prismatic (knife) support 3. cutting edge of a knife or cutter tip of a knife prism (scales) > to be ...
    Large English-Russian Dictionary
  • KNIFE-EDGE - noun. 1) knife edge; smb. sharp cutting 2) supporting prism (scales, etc.) 3) ridge (mountains, dunes, glacier, etc.)
    Large English-Russian Dictionary
  • GIB - I noun; decrease from Gilbert cat Syn: tomcat II noun; those. wedge, counter wedge; gib; gib arm bar ≈ ...
    Large English-Russian Dictionary
  • EDGE - 1. noun. 1) a) edge, edge; edge, border cutting edge ≈ sharp edge jagged, ragged edge ≈ jagged edge at, ...
    Large English-Russian Dictionary
  • DOWNSTREAM TOE OF DAM - 1. a thrust prism of the downstream slope of a dam; drainage prism of the downstream slope of the dam; bottom tooth of the dam 2. bottom [lower edge] of the bottom slope ...
    Large English-Russian Dictionary
  • ANALYSER - noun 1) analyzer (electronic device) 2) tester 3) physical. scattering prism ∙ Syn: analyzer analyzer tester (physical) scattering prism ...
    Large English-Russian Dictionary
  • STELLA OCTANGULA - lat. octagonal star; stellated octahedron
  • PRISM - 1) prism 2) prism-reflector 3) prismatic 4) prismatic. prism of the second order - prism of the second kind prism over polyhedron - prism over the polyhedron right truncated ...
    English-Russian scientific and technical dictionary
  • OCTAGONAL PRISM - math. octagonal prism
    English-Russian scientific and technical dictionary
  • OCTAGONAL INSERT - octagonal cutting insert
    Modern English-Russian dictionary of mechanical engineering and production automation
  • OPTICAL - devices in which radiation from any region of the spectrum (ultraviolet, visible, infrared) is transformed (transmitted, reflected, refracted, polarized). Paying tribute to historical tradition, optical...
    Russian Dictionary Colier
  • POLYHEDON - a part of space limited by a set of a finite number of flat polygons (see GEOMETRY), connected in such a way that each side of any polygon is a side ...
    Russian Dictionary Colier

A direct prism is a body whose two faces (base) are triangles, quadrangles or polygons, and all the rest (lateral) – rectangles (Fig. 104). The rectangular parallelepiped discussed earlier can be classified as a prism: it is a straight prism with rectangular bases. If the bases of a right prism are triangles, then the prism is “triangular”; if it is a square, then the prism is “square”; if quadrangles at all, then “quadrangular”; if any polygons, then “polygonal”, for example. “octagonal”, etc.

We already know how to calculate the volume of a rectangular prism, that is, a rectangular parallelepiped: to do this, we need to multiply its length by its width and height. Since the product of the length of a rectangle by its width gives its area, we can state the previous rule differently, namely this way:

about volumetric rectangular prism

Equal to the product of the area of ​​its base and its height. If the base area of ​​such a prism is denoted by s, and the height – through h, then its volume V= sh.

You can be sure that the same formula applies to any straight prism, no matter what shape its base has. Indeed, for each square centimeter of the base of a straight prism rests a pillar whose height is equal to the height of the prism ( h). All these pillars taken together make up the volume of the prism. But the volume of each column is 1 square. cm H h cm = h cube cm; the number of pillars is equal to the number of squares. cm, contained in the base of the prism. If the base area is 5 sq. cm, then the number of prisms will be s, and the sum of their volumes s? h= sh cube cm. This will be the volume of the prism.

The volume of all direct prisms is equal to the product of area rebuilt at a height.

Repeat questions

What is a straight prism? – What is a right rectangular prism? Square? Triangular? Hexagonal? – How is the volume of any right prism calculated? – Express this rule in a formula.

Applications

31. Calculate the volume of a right triangular prism if its height is 16 cm, and the triangle lying at the base of the prism has a base of 7 cm and a height of 5 cm.

Solution: Let's start calculating the volume by determining the area of ​​the base; it is equal to 0.5 7 5 = 18 square meters. cm. By multiplying the base of the prism by the height, 18 16, we find out its volume - 290 cubic meters. cm.

32. The attic space (Fig. 105) has the shape of a straight triangular prism. Its length is 14 m, its width is 8.1 m, and its ridge height is 3.2 meters. Find the volume (“cubic capacity”) of this room.

Solution: The cubic capacity is 1/2 ? 8,1 ? 3,2 ? 14 = 180 cu. m.

33. What is the area of ​​the base of a straight polyhedral prism, the volume of which is 720 cubic meters? cm, and the height is 18 cm?

Solution: The base is determined by dividing the volume (720) by the height (18). We get 40 cm.

“Prism 10th grade” - Using prisms in everyday life. Prism. Sp.p = Sside + 2Sbase Application of prism in architecture. Formulas for finding area. Correct. The side faces are rectangles. A prism is a polyhedron whose faces are in parallel planes. Sside = Base + h For a straight prism: Sp.p = Pbas. h + 2Sbas.

“Prism polyhedra” - In the 60s of the 17th century, Isaac Newton conducted experiments with light. Questions. ABCDA1B1C1D1 – parallelepiped, convex polyhedron. What physical phenomenon was discovered by I. Newton using a triangular prism? The concept of a polyhedron. ABCDMP is an octahedron made up of eight triangles. Non-convex polyhedron.

“Prism geometry” - Introduction Prism in ancient times Prism in geometry Theorems Problems Sources used. Given a right quadrangular prism ABCDA1B1C1D1. Perpendicular section. A prism whose base is a parallelogram is called a parallelepiped. Thus, the volume of the original prism is equal to the product S h. Solution: Let CM be a perpendicular drawn from point C to plane BC1D.

“Prism volume” - Straight prism. Task. Drawing the altitude of triangle ABC. Study of the theorem about the volume of a prism. Basic steps in proving the direct prism theorem? Area S of the base of the original prism. Questions. Volume of a straight prism. How to find the volume of a straight prism? The solution of the problem. The volume of the original prism is equal to the product S · h.

“Angle between a straight line and a plane” - In the regular 6th prism A...F1, the edges of which are equal to 1, find the angle between the straight line AA1 and the plane ACD1. In the regular 6th prism A...F1, the edges of which are equal to 1, find the angle between straight line AB1 and plane ABD1. In the regular 6th prism A...F1, whose edges are equal to 1, find the angle between straight line AD1 and plane ABC.