Solid geometry

Июль 22, 2022

Содержание

2. Pyramid and its elements Definition Main formulas Problems Examples Truncated pyramid
3. A convex polyhedron with one face a convex polygon (the base) and the vertices of the
4. A right-regular pyramid is one in which the base is a regular polygon and the remaining
5. A regular tetrahedron has equilateral triangles as its faces, and so all its edges have the
6. A pyramid which angles between lateral faces and base are equal
7. A pyramid which angles between edges and base are equal
8. The elements of pyramid Base Vertex Edge Lateral face
9. h - height m - apothem l – lateral edge r – inscribed radius R –
10. The examples of Pyramid in real life
11. Pyramid of life
12. The comparison of world’s pyramids
13. The Surface Area and Volume of an arbitrary Pyramid Base Area Lateral surface Area What does
14. Volume of a pyramid: Lateral Surface Area of a right-regular pyramid: (m-apothem): Tetrahedron (a solid figure
15. The definition of Truncated pyramid A convex polyhedron with one face a convex polygon (the base)
16. Truncated pyramid 1. Show the lateral face area in a truncated pyramid. 2. For regular truncated
17. Problems 3D examples Problem #1 Problem #2 Problem #3 Problem #4 Problem #5 Problem #6 Problem
18. Problem #1 All lateral edges in a triangular pyramid equal , the sides of the base
19. A right triangle which legs are 6 and 8 is the base of a pyramid. All
20. A rhombus which side is 14 and acute angle equals 60˚ is the base of a
21. Prism and its elements Definition Main formulas Problems Examples
22. Examples
23. A convex polyhedron with two “end” faces that are congruent convex polygons lying in parallel planes
24. A right-regular prism is one in which the two end faces are regular polygons and the
25. The types of Prism. Parallelepiped A parallelepiped is a prism in which the two end faces
26. The types of Prism A cube is a right parallelepiped in which all edges are equal.
27. The types of Prism A quadrilateral prism A right-regular hexagonal prism Make the definitions of the
28. Prism and its elements
29. Surface area and Volume of a Prism
30. Cylinder and its elements Definition Main formulas Problems Examples
31. Examples
32. Examples
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Pyramid and its elements
Definition
Main formulas
Problems
Examples
Truncated pyramid

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A convex polyhedron with one face a convex polygon (the base)

and the vertices of the base joined by edges to one other vertex is called a PYRAMID.
The remaining faces are all triangular.

The definition of Pyramid

Pyramid

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A right-regular pyramid is one in which the base is a

regular polygon and the remaining faces are isosceles triangles

The types of Pyramids

A right-regular hexagonal pyramid

A right-regular square pyramid

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A regular tetrahedron has equilateral triangles as its faces, and so

all its edges have the same length

The types of Pyramids

A regular tetrahedron

A right tetrahedron

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A pyramid which angles between lateral faces and base are

equal

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A pyramid which angles between edges and base are equal

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The elements of pyramid
Base
Vertex
Edge
Lateral face

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h - height
m - apothem
l – lateral edge
r – inscribed radius
R

– circumscribed
radius

γ -a dihedral angle on a lateral edge

α –a dihedral angle on the base

β –an angle between an edge and the base

The elements of pyramid

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The examples of Pyramid in real life

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Pyramid of life

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The comparison of world’s pyramids

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The Surface Area and Volume of an arbitrary Pyramid
Base Area
Lateral

surface Area

What does the Base Area of a pyramid depend on?

2. How to calculate the Lateral Surface Area in a pyramid?

3. How to calculate the Total Surface area of a pyramid?

SU13

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Volume of a pyramid:
Lateral Surface Area of a right-regular pyramid: (m-apothem):
Tetrahedron

(a solid figure bounded by four triangular faces. A regular tetrahedron has equilateral triangles as its faces) a - a side:

The Surface Area and Volume of an arbitrary Pyramid

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The definition of Truncated pyramid
A convex polyhedron with one face a

convex polygon (the base) and the vertices of the base joined by edges to one other vertex is called a PYRAMID.
The remaining faces are all triangular.

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Truncated pyramid
1. Show the lateral face area in a truncated pyramid.
2.

For regular truncated pyramid (P1 and P2 are the perimeters of pyramid’s bases, m is an apothem):

3. How to find the TSA of a truncated pyramid?

4. Volume:

Truncated pyramid

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Problems
3D examples
Problem #1
Problem #2
Problem #3
Problem #4
Problem #5
Problem #6
Problem #7
Problem #8
Problem #9

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Problem #1
All lateral edges in a triangular pyramid equal , the

sides of the base are 10, 10 and 12. Find the height of the pyramid.

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A right triangle which legs are 6 and 8 is the

base of a pyramid. All dihedral angles on the base equal 60˚. Find h.

Problem #2

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A rhombus which side is 14 and acute angle equals 60˚

is the base of a pyramid. Dihedral angles on the base are 45˚. Find V.

Problem #3

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Prism and its elements
Definition
Main formulas
Problems
Examples

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Examples

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A convex polyhedron with two “end” faces that are congruent convex

polygons lying in parallel planes in such a way that, with edges joining corresponding vertices.
The remaining faces are parallelograms

The definition of Prism

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A right-regular prism is one in which the two end faces

are regular polygons and the remaining faces are rectangular.

A right-regular triangular prism

The types of Prism

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The types of Prism. Parallelepiped
A parallelepiped is a prism in which

the two end faces (bases) are parallelograms.
A right parallelepiped is one in which 4 lateral faces are rectangles, otherwise its inclined.

A right parallelepiped

An inclined parallelepiped

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The types of Prism
A cube is a right parallelepiped in which

all edges are equal.

A Cube

A rectangular parallelepiped is a right parallelepiped in which the bases are rectangles

A rectangular parallelepiped

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The types of Prism
A quadrilateral prism
A right-regular hexagonal prism
Make

the definitions of the following solids

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Prism and its elements

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Surface area and Volume of a Prism

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Cylinder and its elements
Definition
Main formulas
Problems
Examples

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Examples

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Examples

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Solid geometry

Содержание

Pyramid and its elementsDefinitionMain formulasProblemsExamplesTruncated pyramid

A convex polyhedron with one face a convex polygon (the base)

A right-regular pyramid is one in which the base is a

A regular tetrahedron has equilateral triangles as its faces, and so

A pyramid which angles between lateral faces and base are

A pyramid which angles between edges and base are equal

The elements of pyramidBaseVertexEdgeLateral face

h - heightm - apotheml – lateral edger – inscribed radiusR

The examples of Pyramid in real life

Pyramid of life

The comparison of world’s pyramids

The Surface Area and Volume of an arbitrary PyramidBase Area Lateral

Volume of a pyramid:Lateral Surface Area of a right-regular pyramid: (m-apothem):Tetrahedron

The definition of Truncated pyramidA convex polyhedron with one face a

Truncated pyramid1. Show the lateral face area in a truncated pyramid.2.

Problems3D examplesProblem #1Problem #2Problem #3Problem #4Problem #5Problem #6Problem #7Problem #8Problem #9

Problem #1All lateral edges in a triangular pyramid equal , the

A right triangle which legs are 6 and 8 is the

A rhombus which side is 14 and acute angle equals 60˚

Prism and its elementsDefinitionMain formulasProblemsExamples

Examples

A convex polyhedron with two “end” faces that are congruent convex

A right-regular prism is one in which the two end faces

The types of Prism. ParallelepipedA parallelepiped is a prism in which

The types of PrismA cube is a right parallelepiped in which

The types of PrismA quadrilateral prism A right-regular hexagonal prism Make

Prism and its elements

Surface area and Volume of a Prism

Cylinder and its elementsDefinitionMain formulasProblemsExamples

Examples

Examples

Похожие презентации

Pyramid and its elements
Definition
Main formulas
Problems
Examples
Truncated pyramid

The elements of pyramid
Base
Vertex
Edge
Lateral face

h - height
m - apothem
l – lateral edge
r – inscribed radius
R

The Surface Area and Volume of an arbitrary Pyramid
Base Area
Lateral

Volume of a pyramid:
Lateral Surface Area of a right-regular pyramid: (m-apothem):
Tetrahedron

The definition of Truncated pyramid
A convex polyhedron with one face a

Truncated pyramid
1. Show the lateral face area in a truncated pyramid.
2.

Problems
3D examples
Problem #1
Problem #2
Problem #3
Problem #4
Problem #5
Problem #6
Problem #7
Problem #8
Problem #9

Problem #1
All lateral edges in a triangular pyramid equal , the

Prism and its elements
Definition
Main formulas
Problems
Examples

The types of Prism. Parallelepiped
A parallelepiped is a prism in which

The types of Prism
A cube is a right parallelepiped in which

The types of Prism
A quadrilateral prism
A right-regular hexagonal prism
Make

Cylinder and its elements
Definition
Main formulas
Problems
Examples