3D Figures
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This document defines and provides examples of different 3D shapes (polyhedra and non-polyhedra). It explains that polyhedra are solid figures with polygon faces, while prisms have two parallel congruent bases and pyramids have one base. Examples are given for naming polyhedra based on their base shape and whether they are a prism or pyramid. The document also describes how to construct nets (unfolded shapes) for prisms and pyramids.
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Three dimensional figures
This document defines and describes various three-dimensional figures. It begins by defining 3D figures as solid objects that have length, width, and height. The parts of 3D figures are then identified as surfaces, faces, bases, edges, corners, and vertices. Examples are provided of common 3D shapes like cubes, spheres, cones, cylinders, pyramids, and rectangular prisms along with their characteristics and real-world examples. The document aims to build understanding of 3D geometry terms and the attributes of different three-dimensional shapes.
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This document defines and provides examples of polyhedrons, which are 3D shapes with polygon faces. It lists common polyhedrons like cubes, cuboids, spheres, cones, and cylinders. It provides the key definitions of vertices, faces, and edges. Examples are given for cubes, cuboids, pyramids, cylinders, and cones showing their number of faces, edges, and vertices. Nets for representing the shapes of cubes, cuboids, pyramids, cylinders, and cones are also described.
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This document defines and describes basic solid figures and their components. It explains that a solid figure is a 3D object with length, width, and height or thickness. The key parts are faces, edges where faces meet, and vertices where three or more faces connect. It provides examples of prisms and pyramids, which are named after the shape of their base, and mentions curved surface solids.
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The document discusses three-dimensional shapes and their properties. It defines 3D shapes as having length, width and height. Various 3D shapes are described such as cuboids, cubes, prisms, cylinders, spheres, pyramids and polyhedra. Specific 3D shapes like triangular prisms and hexagonal prisms are defined by their faces, corners and edges. The document asks the reader to identify 3D shapes from different net diagrams.
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A solid figure occupies space and has length, width and height. It has flat surfaces called faces and lines where faces meet called edges. The point where edges meet is a vertex. Prisms have two parallel congruent polygon bases and rectangular faces joining the bases. Pyramids have one polygon base and triangular faces joining at a common vertex. Some solids like cylinders, cones and spheres have curved surfaces instead of faces.
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The document defines and provides information about common 3D shapes including their key features, number of faces, edges, corners, and planes of symmetry. It discusses the cuboid, cube, prism, triangular prism, hexagonal prism, cylinder, cone, sphere, square-based pyramid, tetrahedron, octahedron, dodecahedron, and icosahedron. For each shape, it specifies characteristics like the type of faces, symmetry properties, and whether they are considered prisms.
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This document defines and describes various three-dimensional figures. It begins by defining 3D figures as solid objects that have length, width, and height. The parts of 3D figures are then identified as surfaces, faces, bases, edges, corners, and vertices. Examples are provided of common 3D shapes like cubes, spheres, cones, cylinders, pyramids, and rectangular prisms along with their characteristics and real-world examples. The document aims to build understanding of 3D geometry terms and the attributes of different three-dimensional shapes.
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This document defines and provides examples of polyhedrons, which are 3D shapes with polygon faces. It lists common polyhedrons like cubes, cuboids, spheres, cones, and cylinders. It provides the key definitions of vertices, faces, and edges. Examples are given for cubes, cuboids, pyramids, cylinders, and cones showing their number of faces, edges, and vertices. Nets for representing the shapes of cubes, cuboids, pyramids, cylinders, and cones are also described.
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A solid figure occupies space and has length, width and height. It has flat surfaces called faces and lines where faces meet called edges. The point where edges meet is a vertex. Prisms have two parallel congruent polygon bases and rectangular faces joining the bases. Pyramids have one polygon base and triangular faces joining at a common vertex. Some solids like cylinders, cones and spheres have curved surfaces instead of faces.
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The document discusses visualizing solid figures through identifying their key characteristics such as number of faces, edges, and vertices. It provides examples of different plane and solid figures, describing properties like spheres having one curved face and no edges or vertices, while cubes have six square faces, eight vertices and twelve edges. The document also contrasts polyhedrons which have flat surfaces from solids like spheres with curved surfaces. Students are asked questions to test their understanding of classifying shapes based on these dimensional and geometric properties.
Properties of 2_d_3d_shapes
This document describes properties of two-dimensional and three-dimensional shapes. It defines key terms like faces, edges, vertices, parallel and perpendicular lines. It then discusses properties of common 3D shapes like cubes, cuboids, spheres, pyramids and cylinders. It notes which shapes have some perpendicular/parallel faces and edges. The document also covers types of 2D shapes including polygons, quadrilaterals, circles and triangles.
Properties of 2_d_3d_shapes
The document defines and describes various two-dimensional and three-dimensional shapes. It discusses properties such as faces, edges, vertices, parallel and perpendicular lines. Specific shapes described include cubes, cuboids, spheres, hemispheres, cones, cylinders, pyramids and prisms. Plane shapes such as polygons, quadrilaterals, rectangles, kites, rhombuses and trapezoids are also defined.
MATHEMATICS GRADE 6 Quarter 3 Week 1.pptx
The document defines key terms used to describe solid figures including faces, edges, vertices, and bases. It provides examples of different types of solid figures such as spheres, rectangular prisms, cones, cylinders, pyramids, cubes, and triangular prisms; describing their distinguishing characteristics such as the number and shape of faces, edges, vertices, and bases.
TYPES OF SHAPES
This document defines and describes various two-dimensional and three-dimensional shapes. It explains key properties such as the number of dimensions, faces, edges, vertices and whether shapes have parallel or perpendicular sides. Specific shapes defined include cubes, spheres, cones, cylinders and pyramids. Plane shapes such as polygons, quadrilaterals, rectangles and triangles are also explained.
INTRODUCING TO TYPES OF SHAPES
This document defines and describes various two-dimensional and three-dimensional shapes. It explains key properties such as the number of dimensions, faces, edges, vertices and whether shapes have parallel or perpendicular sides. Specific shapes defined include cubes, spheres, cones, cylinders and pyramids. Plane shapes such as polygons, quadrilaterals, rectangles and triangles are also explained.
Fdocuments.in projection of-solids-complete
The document discusses different types of solids and their properties. It describes solids as three-dimensional figures bounded by plane surfaces. The five Platonic solids are defined as regular polyhedrons with identical regular polygon faces and the same number of faces meeting at each vertex. Prisms and pyramids are also described, with prisms having two identical polygon bases and pyramids having one polygon base and triangular lateral faces meeting at a vertex. Solids of revolution like cylinders and cones are formed by rotating a curve around an axis. Projection of solids involves drawing their views in different orientations.
Visualizing solid shapes!!!
This document discusses different types of 2D and 3D shapes. It describes 2D shapes as flat objects defined by straight or curved lines, including polygons like triangles and squares. 3D shapes have length, width, and height, enclosing a volume. They are characterized by faces, vertices, and edges. The document contrasts 2D and 3D properties, provides examples of 3D shapes like cubes and pyramids, and defines key 3D geometric terms such as faces, edges, and vertices.
One's own work
A prism is a three-dimensional solid shape that has two identical and parallel bases joined by rectangular faces. It has flat faces and the same cross-sectional shape along its entire length. Prisms can have different cross-sectional shapes including squares, rectangles, triangles, pentagons and more. They are classified as regular if the cross-sectional shape is regular, or irregular if the cross-section is irregular. The surface area of a prism is calculated as two times the base area plus the base perimeter multiplied by the length. Its volume equals the area of one base multiplied by the length of the prism.
Plane figures
The document defines and describes various plane figures (two-dimensional shapes). It begins by defining what a plane figure is and then describes the key properties of circles, triangles, rectangles, rhombuses, squares, and trapezoids. For each shape, it provides the defining characteristics, such as a circle tracing a curve that is always the same distance from the center and a triangle being formed by 3 straight lines. It also classifies triangles based on their angles and sides. The document aims to teach the reader to define, identify, and draw the principal geometric plane figures.
Kelompok 7 Geometry Space (BIM).pdf
The document provides information about geometry in 3D space. It discusses polyhedra like prisms, platonic solids, and pyramids. It provides the formulas to calculate the volume and surface area of prisms, platonic solids, pyramids, cylinders, cones, and spheres. It then gives examples of different types of prisms, pyramids, and provides quiz questions to test understanding of volume calculations.
Properties of 2_d_3d_shapes
The document describes various 2D and 3D shapes. It defines key properties such as faces, edges, vertices, parallel and perpendicular lines. It provides examples of common 3D shapes like cubes, spheres, pyramids and discusses which have parallel/perpendicular faces and edges. The document also covers 2D plane shapes including polygons, quadrilaterals and gives examples like rectangles, squares, rhombus. It asks the reader to name shapes with 7, 9 or 10 sides and examples of triangles.
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Surface area of Cylinders and HW
The document discusses the surface area formula for cylinders. It can be found by adding the area of the two circular bases and the lateral rectangular area. The total surface area is given as 2πrh + 2πr^2. Several examples are provided to demonstrate calculating the surface area of cylinders using given radii and heights. One example asks if 175 in^2 of gift wrap will be enough to cover a gift with a cylindrical container that has a height of 18 in and diameter of 3 in.
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The document discusses scientific notation, which is a way to write very large or small numbers in a more compact form using two factors - a number between 1 and 10 multiplied by a power of 10. It provides examples of converting numbers between standard form and scientific notation, such as 2.3 x 103 representing 2300. The Andromeda Galaxy contains at least 200 billion stars, which can be written more concisely in scientific notation as 2 x 1011 stars.
Volume of Prisms
Rectangular and triangular prisms have formulas to calculate their volume (V).
For a rectangular prism, V = (bh)h, where b is the width, h is the height, and the product bh gives the area of the rectangular base.
For a triangular prism, V = (1/2)bh, where b is the base, h is the height. The area of the triangular base is calculated as (1/2)bh.
Both formulas multiply the area of the base by the height to determine the volume of the entire prism.
Circles
This document provides information about calculating the circumference and area of circles. It defines key terms like diameter, radius, circumference, and area. Formulas are provided to calculate circumference using either the diameter or radius. The circumference formula is C=πd or C=2πr. The area formula is A=πr^2. Examples are worked through to find the circumference or area given values for diameter or radius. Readers are prompted to try sample problems applying the formulas.
Area of triangles and trapezoids
The document discusses formulas for calculating the areas of triangles and trapezoids. For triangles, the area formula is 1/2 base × height. For trapezoids, the area formula is 1/2 × (sum of the two bases) × height. Several examples are provided to demonstrate calculating areas using these formulas.
Area and perimeter of parallelograms
This document discusses finding the perimeter and area of squares, rectangles, and parallelograms using formulas. It instructs the reader to look at a formula chart to find the appropriate formulas rather than memorizing them. It provides examples of calculating the perimeter and area of different shapes using the side lengths provided and the correct formulas from the chart. The base and height of any shape always form a right angle within the shape.
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The document discusses translations, which are horizontal and/or vertical slides that move a shape to a new position without changing its size or shape. Translations are determined by a rule that specifies the change in x- and y-coordinates from the original figure to the translated image. Examples are given of translating shapes right, left, up, and down according to translation rules.
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This document contains instructions for reflecting geometric shapes across various lines. It discusses reflecting a pentagon across the x-axis, a triangle across the y-axis, and other shapes across the lines x=3 and y=-2. The final reflection is of an unknown shape across the y-axis.
Data Representations
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The document provides the daily objectives and agenda for a math class over the course of a week. Each day's objective is to model equations to find solutions. The daily agenda includes warm-up problems, homework review, and new vocabulary or concepts. Warm-up problems involve writing algebraic expressions, modeling equations, and defining math terms. Quotes of the day are also provided for inspiration.
Warm-Ups for January 7-11
The document provides daily lesson plans and objectives for a math class over the course of a week. Each day's plan includes: welcoming students, listing objectives and activities for the day, providing a daily quote, and presenting word problems or sequences for students to work on as a warm-up. The weeklong plans focus on using words and symbols to describe arithmetic sequences and using different strategies to solve problems.
Modeling 2 Step Equations
1) The document discusses using algebra tiles to model and solve two-step equations.
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3) The key steps are to first group like terms on each side, then remove common terms from both sides to simplify the equation before solving for the variable.
Modeling one step equations
This document contains symbols and formatting that do not convey clear meaning. It includes white circles, bullet points, and dashes but no discernible words, sentences, or paragraphs that can be succinctly summarized in 3 sentences or less. The content and essential information is unclear from the symbols and characters provided.
Expression Notes
A variable is a symbol that represents a number, while an expression consists of numbers, variables, and operations. Key words in word problems indicate whether to add, subtract, multiply, or divide. Expressions can be written as mathematical statements, and evaluated by substituting values for variables.
Percent Bars
Here are the steps to solve problems like these:
1. Identify the "is", "of", and "%" amounts given in the problem
2. Set up a proportion relating the amounts:
is/of = %/100
3. Solve the proportion algebraically for the missing value
Be sure to show the proportion and substitution steps to arrive at the solution. Drawing a percent bar can also help visualize the relationship between the amounts. Practice these types of problems until you feel comfortable setting up and solving the proportions. Let me know if any specific problems give you trouble.
Sales Tax and Total Cost
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Discount and Sale Price
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October 9 12, 2012
The document outlines the daily agenda and objectives for a classroom, including assignments on operations with decimals, independent study time, a math test, and converting fractions, decimals, and percents. Each day's agenda is introduced with a quote of the day and includes warm-up problems or assignments related to the objective.
Warm-ups Week of October 5, 2012
The document appears to be notes from a math class, listing the daily objectives and math problems for students on different levels. It provides the dates from Monday, October 1st to Friday, October 5th and includes the learning objectives for comparing, ordering, and performing calculations with decimals each day. Motivational quotes are also included at the bottom of each page.
Order of Operations
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2. It explains that the order of operations (PEMDAS) is an agreed upon procedure, not a mathematical fact, to ensure consistency.
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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3D Figures
- 1. Solids Space Figures 3D Shapes
- 2. Polyhedra (pl) or Polyhedron (s) • A solid figure that has polygons for its faces. • A solid figure with a curved surface is NOT a polyhedron!
- 3. Prism (polyhedron) • A solid that has two congruent and parallel bases • All other faces are parallelograms
- 4. Pyramid (polyhedron) • A solid that has only 1 base • All other faces are triangles
- 5. Definitions • Faces – the flat surfaces of the shape • Edges – the line segments that are formed by the faces connecting • Vertices – the corners where the edges meet (sing. – vertex) Vertex Face Edge
- 6. Solids (non-polyhedra) • Cones – 1 base that is a circle • Cylinders – 2 bases that are circles • Spheres – all points equidistance from the center in 3D form
- 7. To name a polyhedron: • First name the shape of the base • Then determine if the shape is a prism or pyramid • The name of the 3-D shape is the combination of the name of the base plus the word “prism” or “pyramid” after it
- 8. You try it…name that shape!
- 10. Basic Construction • Prisms – • Have 2 parallel and congruent bases • The base shape tells you how many other faces you will have • All other faces will be parallelograms • Pyramids • Have 1 base • The base shape will tell you how many other faces you will have • All other faces will be triangles
- 11. How to make a net for a prism. • Draw a rectangle. • Place the base shape on top and one on bottom.
- 12. How to make a net for a prism. • Count the number of sides on the base and have the same number of rectangles
- 13. How to make a net for a prism. • Make certain that you have a base on top and one on bottom, otherwise it does not matter where you place the base shapes.
- 14. How to make a net for a pyramid. • Draw the base shape. The number of sides will tell you how many triangles to add to the shape.
- 15. How to make a net for a pyramid. • Then attach a triangle to each side of the base polygon.
- 16. An alternative way to make a prism.
- 17. You try it…name that shape!
- 18. You try it…name that shape!