Cilindros, Conos, Esferas, prismas y piramides

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en esta actividad vamos a desarrollar una presentación donde mostramos las diferentes partes y propiedades de los cilindros, prismas, piramides,conos y esferas.

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geometria del espacio

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Cilindros, Conos, Esferas, prismas y piramidesVersión en línea en esta actividad vamos a desarrollar una presentación donde mostramos las diferentes partes y propiedades de los cilindros, prismas, piramides,conos y esferas. por Geometría del espacio 1 Cylinder In this image we can see the parts of the cylinder and the formulas to find the total area and its volumen. The cylinder is a solid composed of two congruent circles in parallel, their interiors and all the line segments parallel to the segment containing the center of both circle with endpoints on the circular regions. Radius: (r) the radius is the distance from the center outwards. Altitude: (h) is a perpendicular segment from the plane of one base to the plane of the other. Axis: the axis of the cylinder is the segment containing the center of the two bases. Base: the base is the circular end if the cylinder. Volume: 3.1416* r^2 h Latera area:* 2 \pi rh Circular area: \pi * r^2 Total area: lateral area + circular area Bibliografy Geometry (s.f): right cyrcular cylinder. of https://doza.pro/art/math/geometry/en/cylinder-hollow 2 Cylinder 3 Sphere Aporte the Maryluz hernandez Elements of the sphere. Center: Interior point that is equidistant from any point on the surface of the sphere. Radius: Distance from the center to a point on the surface of the sphere. Chord: Segment that joins two points on the spherical surface. Diameter: chord that passes through the center. Poles: They are the points of the axis of rotation that remain on the spherical surface. Click to see the image. https://drive.google.com/file/d/1I21Ke-k3xIg9_ixdaL7i1_nFZauRTlKs/view?usp=sharing Bibliografy Ceibal, P. (2010). Área y volumen de una esfera. Recuperado de: http://www.ceibal.edu.uy/UserFiles/P0001/ODEA/ORIGINAL/111004_esferas.elp/rea_y_volumen_de_una_esfera.html 4 Sphere Aporte the Maryluz Hernandez My son's soccer ball has a diameter of 20 cm. ¿What is the total area of the Object? Reply As we know that the Diameter is 20 cm. Then your Radius will be. Diameter/2 = 20/2 = 10 cm. Now we apply the formula to find the Area of the sphere. *Área = 43,1416(rr) =1256,54 cm cuadrados. The ball has an area of = 1256,54 cm cuadrados 5 Murillo, M. F. (2002). Consultor estudiantil. Prolibros. Prism A prism is a polyhedron that has two equal faces and the other faces are parallelograms. The equal faces are called bases and the others, lateral faces. The height of a prism is the distance between the two bases. A prism is straight or oblique depending on whether its lateral edges are perpendicular or oblique with respect to the bases. A prism is triangular, pentagonal, rectangular, etc., depending on whether its bases are triangles, quadrilaterals, pentagons, etc. 6 https://www.universoformulas.com/matematicas/geometria/prisma/?fbclid=IwAR0k1JQluegYzlF5o72eHRCz89COYt59wK2_WlJITMZ3QBnCopK40psbQD0 Trunk of prism is the part of the prism between one of the bases and a plane oblique to it, which cuts all the lateral edges. The lateral area of a prism is equal to the product of the lateral edge and the perimeter of the straight section. Volume = Base Area × Length Area = 2 x Ab + Pb x h Area = 2 × Base Area + Base Perimeter × height 7 Prism problem Susana wants to buy a display case in the shape of a square prism to promote her new perfumes, she needs to know the total area and volume it occupies. She knows that the side of the base is 1.05 m and the height is 3 m. Total area = Lateral area + 2 times the Base Area 8 Problem 9 PYRAMID PYRAMID A right pyramid with a regular base has isosceles triangle sides, with symmetry is Cnv or [1,n], with order 2n. It can be given an extended Schläfli symbol ( ) ∨ {n}, representing a point, ( ), joined (orthogonally offset) to a regular polygon, {n}. A join operation creates a new edge between all pairs of vertices of the two joined figuresReferenciahttps://en.wikipedia.org/wiki/Pyramid_(geometry) 10 TYPES OF PYRAMIDS Types Of Pyramids There are different types of pyramids that are named based on the shapes of their bases. Triangular Pyramid Square Pyramid Pentagonal Pyramid Right Pyramid Oblique Pyramid Triangular Pyramid The base of this pyramid has the shape of a triangle; therefore, we call it as a triangular pyramid. Square Pyramid The base of this type of pyramid has a shape of a square; therefore, we call it a Square Pyramid. Pentagonal Pyramid The base of this pyramid has the shape of a Pentagon; therefore, we call it a Pentagonal Pyramid. Right Pyramid The apex of this pyramid is exactly over the middle of the base, hence named as Right Pyramid. Oblique Pyramid The apex of this pyramid is not exactly over the middle of its base and named as Oblique Pyramid. Regular vs Irregular Pyramid To distinguish between regular and irregular Pyramid, you need to consider the shape of the base. If the base of a polygon is regular, it is labelled as Regular Pyramid, else it is considered as Irregular Pyramid. You can see the figures given below for both the pyramids 11 Area and Volume Pyramid The Volume of a Pyramid 1/3 × [Base Area] × Height The Surface Area of a Pyramid When all side faces are the same: [Base Area] + 1/2 × Perimeter × [Slant Length] When side faces are different: [Base Area] + [Lateral Area] 12 PYRAMID 13 Cono Cone It is the geometric body obtained by rotating a right triangle around one of its legs. Elements of the cone. Axis: It is the fixed leg around which the triangle rotates. Base: It is the circle that forms the other leg.. Height: It is the distance from the vertex to the base.. Generatrix:** It is the hypotenuse of the right triangle.. 14 Cone trunk 15 Volumen 16 Problem 17 Solution

Cilindros, Conos, Esferas, prismas y piramidesVersión en línea

en esta actividad vamos a desarrollar una presentación donde mostramos las diferentes partes y propiedades de los cilindros, prismas, piramides,conos y esferas.

Cylinder

In this image we can see the parts of the cylinder and the formulas to find the total area and its volumen. The cylinder is a solid composed of two congruent circles in parallel, their interiors and all the line segments parallel to the segment containing the center of both circle with endpoints on the circular regions.

Radius: (r) the radius is the distance from the center outwards.

Altitude: (h) is a perpendicular segment from the plane of one base to the plane of the other.

Axis: the axis of the cylinder is the segment containing the center of the two bases.

Base: the base is the circular end if the cylinder.

Volume: 3.1416* r^2 *h

Latera area: 2 \pi *r*h

Circular area: \pi * r^2

Total area: lateral area + circular area

Bibliografy

Geometry (s.f): right cyrcular cylinder. of https://doza.pro/art/math/geometry/en/cylinder-hollow

Cylinder

Sphere

Aporte the Maryluz hernandez

Elements of the sphere.

Center: Interior point that is equidistant from any point on the surface of the sphere.

Radius: Distance from the center to a point on the surface of the sphere.

Chord: Segment that joins two points on the spherical surface.

Diameter: chord that passes through the center.

Poles: They are the points of the axis of rotation that remain on the spherical surface.

Click to see the image.

https://drive.google.com/file/d/1I21Ke-k3xIg9_ixdaL7i1_nFZauRTlKs/view?usp=sharing

Bibliografy

Ceibal, P. (2010). Área y volumen de una esfera. Recuperado de: http://www.ceibal.edu.uy/UserFiles/P0001/ODEA/ORIGINAL/111004_esferas.elp/rea_y_volumen_de_una_esfera.html

Sphere

Aporte the Maryluz Hernandez

My son's soccer ball has a diameter of 20 cm.

¿What is the total area of the Object?

Reply

As we know that the Diameter is 20 cm.

Then your Radius will be. Diameter/2 = 20/2 = 10 cm.

Now we apply the formula to find the Area of the sphere.

Área = 4*3,1416*(r*r) =1256,54 cm cuadrados.

The ball has an area of = 1256,54 cm cuadrados

Murillo, M. F. (2002). Consultor estudiantil. Prolibros.

Prism

A prism is a polyhedron that has two equal faces and the other faces are parallelograms. The equal faces are called bases and the others, lateral faces. The height of a prism is the distance between the two bases. A prism is straight or oblique depending on whether its lateral edges are perpendicular or oblique with respect to the bases. A prism is triangular, pentagonal, rectangular, etc., depending on whether its bases are triangles, quadrilaterals, pentagons, etc.

https://www.universoformulas.com/matematicas/geometria/prisma/?fbclid=IwAR0k1JQluegYzlF5o72eHRCz89COYt59wK2_WlJITMZ3QBnCopK40psbQD0

Trunk of prism is the part of the prism between one of the bases and a plane oblique to it, which cuts all the lateral edges. The lateral area of a prism is equal to the product of the lateral edge and the perimeter of the straight section.

Volume = Base Area × Length

Area = 2 x Ab + Pb x h

Area = 2 × Base Area + Base Perimeter × height

Prism problem

Susana wants to buy a display case in the shape of a square prism to promote her new perfumes, she needs to know the total area and volume it occupies. She knows that the side of the base is 1.05 m and the height is 3 m.

Total area = Lateral area + 2 times the Base Area

Problem

PYRAMID

A right pyramid with a regular base has isosceles triangle sides, with symmetry is Cnv or [1,n], with order 2n. It can be given an extended Schläfli symbol ( ) ∨ {n}, representing a point, ( ), joined (orthogonally offset) to a regular polygon, {n}. A join operation creates a new edge between all pairs of vertices of the two joined figuresReferenciahttps://en.wikipedia.org/wiki/Pyramid_(geometry)

TYPES OF PYRAMIDS

Types Of Pyramids

There are different types of pyramids that are named based on the shapes of their bases.

Triangular Pyramid
Square Pyramid
Pentagonal Pyramid
Right Pyramid
Oblique Pyramid

Triangular Pyramid

The base of this pyramid has the shape of a triangle; therefore, we call it as a triangular pyramid.

Square Pyramid

The base of this type of pyramid has a shape of a square; therefore, we call it a Square Pyramid.

Pentagonal Pyramid

The base of this pyramid has the shape of a Pentagon; therefore, we call it a Pentagonal Pyramid.

Right Pyramid

The apex of this pyramid is exactly over the middle of the base, hence named as Right Pyramid.

Oblique Pyramid

The apex of this pyramid is not exactly over the middle of its base and named as Oblique Pyramid.

Regular vs Irregular Pyramid

To distinguish between regular and irregular Pyramid, you need to consider the shape of the base. If the base of a polygon is regular, it is labelled as Regular Pyramid, else it is considered as Irregular Pyramid. You can see the figures given below for both the pyramids

Area and Volume Pyramid

The Volume of a Pyramid

1/3 × [Base Area] × Height

The Surface Area of a Pyramid

When all side faces are the same:

[Base Area] + 1/2 × Perimeter × [Slant Length]

When side faces are different:

[Base Area] + [Lateral Area]

PYRAMID

Cono

Cone

It is the geometric body obtained by rotating a right triangle around one of its legs.

Elements of the cone.

Axis: It is the fixed leg around which the triangle rotates.

Base: It is the circle that forms the other leg..

Height: It is the distance from the vertex to the base..

Generatrix: It is the hypotenuse of the right triangle..

Cilindros, Conos, Esferas, prismas y piramides

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Cilindros, Conos, Esferas, prismas y piramides

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Cilindros, Conos, Esferas, prismas y piramidesVersión en línea

por Geometría del espacio

Cylinder

Cylinder

Sphere

Sphere

Murillo, M. F. (2002). Consultor estudiantil. Prolibros.

Prism

https://www.universoformulas.com/matematicas/geometria/prisma/?fbclid=IwAR0k1JQluegYzlF5o72eHRCz89COYt59wK2_WlJITMZ3QBnCopK40psbQD0

Prism problem

Susana wants to buy a display case in the shape of a square prism to promote her new perfumes, she needs to know the total area and volume it occupies. She knows that the side of the base is 1.05 m and the height is 3 m.

Total area = Lateral area + 2 times the Base Area

Problem

PYRAMID

PYRAMID

TYPES OF PYRAMIDS

Types Of Pyramids

Triangular Pyramid

Square Pyramid

Pentagonal Pyramid

Right Pyramid

Oblique Pyramid

Regular vs Irregular Pyramid

Area and Volume Pyramid

The Volume of a Pyramid

The Surface Area of a Pyramid

PYRAMID

Cono

Cone trunk

Volumen

Problem

Solution