OVERVIEW

Blogging is one of a valuable tool in the 21^st century for it provides deeper understanding of ethnical culture by incorporating an iterative method of research, reflection and action process. Teachers being the implementers of learning should provide lessons that are not only confined in the four corners of the room but gives opportunity for students to explore, create, innovate and share.

            “MSU Taking the Lead to the 21^st Century School Teaching “ is a weblog project of MSU-BSED students who are taking Educational Technology 2 (ED 105B). The project helps students develop their creativity, research and writing ability, enhances environmental awareness, leadership, social responsibility, initiatives as well as better technological and communication skills. 

TRIVIA!!!!!!!!!!!!

Space figures and basic solids

Space figures
Cross-section
Volume
Surface area
Cube
Cylinder
Sphere
Cone
Pyramid
Tetrahedron
Prism

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Space Figure

A space figure or three-dimensional figure is a figure that has depth in addition to width and height. Everyday objects such as a tennis ball, a box, a bicycle, and a redwood tree are all examples of space figures. Some common simple space figures include cubes, spheres, cylinders, prisms, cones, and pyramids. A space figure having all flat faces is called a polyhedron. A cube and a pyramid are both polyhedrons; a sphere, cylinder, and cone are not.

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Cross-Section

A cross-section of a space figure is the shape of a particular two-dimensional "slice" of a space figure.
Example:
The circle on the right is a cross-section of the cylinder on the left.

The triangle on the right is a cross-section of the cube on the left.

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Volume

Volume is a measure of how much space a space figure takes up. Volume is used to measure a space figure just as area is used to measure a plane figure. The volume of a cube is the cube of the length of one of its sides. The volume of a box is the product of its length, width, and height.
Example:
What is the volume of a cube with side-length 6 cm?
The volume of a cube is the cube of its side-length, which is 6³ = 216 cubic cm.
Example:
What is the volume of a box whose length is 4cm, width is 5 cm, and height is 6 cm?
The volume of a box is the product of its length, width, and height, which is 4 × 5 × 6 = 120 cubic cm.

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Surface Area

The surface area of a space figure is the total area of all the faces of the figure.
Example:

What is the surface area of a box whose length is 8, width is 3, and height is 4? This box has 6 faces: two rectangular faces are 8 by 4, two rectangular faces are 4 by 3, and two rectangular faces are 8 by 3. Adding the areas of all these faces, we get the surface area of the box:
8 × 4 + 8 × 4 + 4 × 3 + 4 × 3 + 8 × 3 + 8 × 3 = 
32 + 32 + 12 + 12 +24 + 24= 
136.

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Cube

A cube is a three-dimensional figure having six matching square sides. If L is the length of one of its sides, the volume of the cube is L³ = L × L × L. A cube has six square-shaped sides. The surface area of a cube is six times the area of one of these sides.
Example:
The space figure pictured below is a cube. The grayed lines are edges hidden from view.

Example:
What is the volume and surface are of a cube having a side-length of 2.1 cm?
Its volume would be 2.1 × 2.1 × 2.1 = 9.261 cubic centimeters.
Its surface area would be 6 × 2.1 × 2.1 = 26.46 square centimeters.

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Cylinder

A cylinder is a space figure having two congruent circular bases that are parallel. If L is the length of a cylinder, and r is the radius of one of the bases of a cylinder, then the volume of the cylinder isL × pi × r², and the surface area is 2 × r × pi × L + 2 × pi × r².
Example:
The figure pictured below is a cylinder. The grayed lines are edges hidden from view.

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Sphere

A sphere is a space figure having all of its points the same distance from its center. The distance from the center to the surface of the sphere is called its radius. Any cross-section of a sphere is a circle. 
If r is the radius of a sphere, the volume V of the sphere is given by the formula V = 4/3 × pi ×r³. The surface area S of the sphere is given by the formula S = 4 × pi ×r².
Example:
The space figure pictured below is a sphere.

Example:
To the nearest tenth, what is the volume and surface area of a sphere having a radius of 4cm?
Using an estimate of 3.14 for pi, 
the volume would be 4/3 × 3.14 × 4³ = 4/3 × 3.14 × 4 × 4 × 4 = 268 cubic centimeters.
Using an estimate of 3.14 for pi, the surface area would be 4 × 3.14 × 4² = 4 × 3.14 × 4 × 4 = 201 square centimeters.

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Cone

A cone is a space figure having a circular base and a single vertex. 
If r is the radius of the circular base, and h is the height of the cone, then the volume of the cone is 1/3 × pi × r² × h.
Example:
What is the volume in cubic cm of a cone whose base has a radius of 3 cm, and whose height is 6 cm, to the nearest tenth? 
We will use an estimate of 3.14 for pi.
The volume is 1/3 × pi × 3² × 6 = pi ×18 = 56.52, which equals 56.5 cubic cm when rounded to the nearest tenth.
Example:
The pictures below are two different views of a cone.

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Pyramid

A pyramid is a space figure with a square base and 4 triangle-shaped sides.
Example:
The picture below is a pyramid. The grayed lines are edges hidden from view.

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Tetrahedron

A tetrahedron is a 4-sided space figure. Each face of a tetrahedron is a triangle.
Example:
The picture below is a tetrahedron. The grayed lines are edges hidden from view.

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Prism

A prism is a space figure with two congruent, parallel bases that are polygons.
Examples:
The figure below is a pentagonal prism (the bases are pentagons). The grayed lines are edges hidden from view.

The figure below is a triangular prism (the bases are triangles). The grayed lines are edges hidden from view.

The figure below is a hexagonal prism (the bases are hexagons). The grayed lines are edges hidden from view..

QUIZBEE!!

 

Plane and Space Figures

Quiz

Choose the correct answer.

 1 / 14  

1. What is this figure?
   
   1.   square
   2.   pyramid
   3.   triangle
   4.   pentagon

 

GEOMETRIC SHAPES

PLANR FIGURES

t surfaces such as walls, desk tops, floors, and paper are planes. Planes are everywhere around you.

 

A flat, closed figure that is in a plane is called a plane figure. A plane figure can be made of straight lines, curved lines, or both straight and curved lines.

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Look at the figures and click on the ones that are plane figures. Remember that a plane figure is closed and has straight or curved lines.

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Look at these figures and decide if they are made of straight lines, curved lines or both straight and curved lines.

curved    straight    both     curved    straight    both     curved    straight    both     curved    straight    both  |

 

Some letters of the alphabet are plane figures. See if you can decide which letters are plane figures. Remember that a plane figure is a flat, closed, shape in a plane.

Click on the letters you think are plane figures.     |

 

All of these everyday shapes are plane figures.

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Some plane figures have all straight sides and angles. The number of sides and angles will be the same.

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Look at the following figures and tell how many sides and angles each one has.       Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8 Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8 Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8 Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8       Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8 Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8 Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8 Sides:      1    2    3    4    5    6    7    8  Angles:      1    2    3    4    5    6    7    8  |

 

Now let’s see if you can find out how many lines and angles are in these everyday objects. Type in the number of lines and the number of angles.

Sides:   0    1    2    3    4    5    6    7    8       Angles:   0    1    2    3    4    5    6    7    8      Sides:   0    1    2    3    4    5    6    7    8       Angles:   0    1    2    3    4    5    6    7    8      Sides:   0    1    2    3    4    5    6    7    8       Angles:   0    1    2    3    4    5    6    7    8       |

 

Plane figures are flat, closed, figures that are in a plane. Look around your room for plane figures. Get a sheet of paper and draw and label 4 plane figures with 4 different shapes.  Plane figures are all around you !

space figures

The space that we live in has three dimensions: length, width, and height. Three-dimensional geometry, or space geometry, is used to describe the buildings we live and work in, the tools we work with, and the objects we create.First, we'll look at some types of polyhedrons. A polyhedron is a three-dimensional figure that has polygons as its faces. Its name comes from the Greek "poly" meaning "many," and "hedra," meaning "faces." The ancient Greeks in the 4th century B.C. were brilliant geometers. They made important discoveries and consequently they got to name the objects they discovered. That's why geometric figures usually have Greek names!
We can relate some polyhedrons--and other space figures as well--to the two-dimensional figures that we're already familiar with. For example, if you move a vertical rectangle horizontally through space, you will create a rectangular or square prism.

If you move a vertical triangle horizontally, you generate a triangular prism. When made out of glass, this type of prism splits sunlight into the colors of the rainbow.

Now let's look at some space figures that are not polyhedrons, but that are also related to familiar two-dimensional figures. What can we make from a circle? If you move the center of a circle on a straight line perpendicular to the circle, you will generate a cylinder. You know this shape--cylinders are used as pipes, columns, cans, musical instruments, and in many other applications.

A cone can be generated by twirling a right triangle around one of its legs. This is another familiar space figure with many applications in the real world. If you like ice cream, you're no doubt familiar with at least one of them!

A sphere is created when you twirl a circle around one of its diameters. This is one of our most common and familiar shapes--in fact, the very planet we live on is an almost perfect sphere! All of the points of a sphere are at the same distance from its center.

There are many other space figures--an endless number, in fact. Some have names and some don't. Have you ever heard of a "rhombicosidodecahedron"? Some claim it's one of the most attractive of the 3-D figures, having equilateral triangles, squares, and regular pentagons for its surfaces. Geometry is a world unto itself, and we're just touching the surface of that world. In this unit, we'll stick with the most common space figures.