3-Dimensional Figures
3-dimensional figures are shapes that have three dimensions: length, width, and height. Common examples include cubes, spheres, cones, and pyramids. These figures are often represented in geometry and can be visualized in physical space. They are characterized by their volume, surface area, and the number of faces, edges, and vertices they possess.
7 Key excerpts on "3-Dimensional Figures"
eBook - ePubThe Path To Early Math
What Preschool Teachers Need to Know
- Ingrid Crowther(Author)
- 2021(Publication Date)
- Gryphon House Inc.(Publisher)
...CHAPTER 8: Two-and-Three Dimensional Geometric Shapes “Investigating and exploring shape and space is an inherent part of children’s mathematical development. If you observe the young child playing freely in an outdoor environment, their ability to navigate obstacles, lift, move, or stack objects, or push and pull items are all examples of geometry that come naturally to them.” —Juliet Robertson, Messy Maths: A Playful Outdoor Approach Geometric Shapes Defined I n defining geometric shapes, we consider reasoning about the shape, thinking about how the shapes relate to one another, and thinking about how shapes are perceived in space. Reasoning about geometric shapes means looking at the physical attributes of different shapes: The number of vertices or points, such as three points in a triangle Straight or curved lines, such as those in rectangles or ovals The number of sides a shape has, such as eight sides to an octagon Whether the shapes are flat or curved (2-D or 3-D), such as a circle or a sphere The second component, thinking about how shapes relate to each other, involves looking at them and seeing how they fit together. For example, two identical squares when placed together form a rectangle, and two identical isolate triangles (triangles with two equal sides) form a rhombus when placed together. It’s also important to look at how shapes are perceived in space. This requires children to learn some of the spatial terminology that supports these perceptions...
- Sandra Rush(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...Solid lines indicate edges that you actually see, and dashed lines indicate edges that are obscured from the two-dimensional perspective. Edges are the lines where two faces (flat surfaces) meet on a three-dimensional figure. On the figure shown below, the “main” face is shaded and the arrows indicate which way the figure is facing. It takes a while to get used to this way of looking at three-dimensional figures. The GED ® test formula sheet provides the formulas you will need to do surface area and volume problems with three-dimensional figures. Still, you need to know what these terms mean as well as what the variables in the given equation mean or the formulas won’t be of any use to you. Therefore, this section on three-dimensional figures provides information to help you understand the GED ® test formula sheet, but it isn’t necessary to memorize the formulas. The surface area of a three-dimensional figure is exactly what it sounds like. It is the total area of all the faces, even those you cannot see in the picture. So for surface area, we need to remember the formulas for the areas of the two-dimensional faces that make up each three-dimensional figure. Again, these are given on the GED ® test formula sheet. The surface area of a rectangular solid can be thought of as the area of wrapping paper that covers a shirt box with no overlapping. Volume is how much the three-dimensional figure can hold. It is sometimes called capacity. Basically, for three-dimensional figures that have identical “tops” and “bottoms” (bases), it is the area of the base (bottom or top) multiplied by the height of the figure. Note the dimensions for each measure. Although feet are shown here, you can substitute “inches,” “centimeters,” or whatever the problem is using. Note that the power (exponent) matches the number of the dimensions of the figure. Rectangular Prisms One type of three-dimensional figure is known as a rectangular prism, which is also referred to as a right prism...
- Lyn Dawes(Author)
- 2013(Publication Date)
- Routledge(Publisher)
...Some of the Talking Points are ‘correct’ in mathematical terms. The discussion then focuses on how the group can explain the idea to one another – and the class. Talking Points: 2D and 3D Shapes Talking Points Think together to decide together whether these ideas are true or false – or if you are unsure. Discuss everyone’s suggestions. Draw an example that shows what you think. If the angles of a triangle are all equal, the sides all have to be equal too. We can name a quadrilateral that has no parallel sides. A rhombus is a squashed square. Irregular polygons have sides of different lengths. A cube has six faces (sides), six edges and six vertices (corners). There is more than one 3D shape that has no edges or vertices. We can fold a piece of paper to make a pentagon. There is a 3D shape that fits this description: five flat surfaces, one of them a square. We can say what shape the other four faces are. The word ‘straight’ is the opposite of the word ‘curved’. A degree is a unit that measures angle. The perimeter of a hexagon is equal to six times the radius of the circumscribed circle. A traffic cone, a fir-tree cone and an ice cream cone all have some things in common with a volcanic cone. A triangular prism has a triangle cross-section any way you cut it. This net will make a triangular prism (see diagram on right). The plural of vertex is vertixes. Talking Points: About the Number 3 Talking Points These Talking Points are facts about the number 3...
- Fuchang Liu(Author)
- 2017(Publication Date)
- Routledge(Publisher)
...After all, the focus of this lesson is perimeter, and you want to get this concept across without your children having to deal with measuring at the same time. “All 3-D Shapes Have an Extra Third Dimension of Height” After her children had enough experience with 2-D shapes, Jane started exposing them to 3-D ones. Naturally, she based her discussion of 3-D shapes on their knowledge of 2-D shapes. She said, “A rectangle is a two-dimensional shape, and it has two dimensions of length and width. A rectangular prism is a three-dimensional shape, and it has three dimensions of length, width, and height. So we can say all three-dimensional shapes have an extra third dimension of height.” But Jane didn’t have a ready answer when a child asked, “When I look at a triangle, it’s a two-dimensional shape and its two dimensions are base and height. Now if I have a triangular prism, it’s a three-dimensional shape. Then what’s its third dimension? Is it another height? If so, how is it different from the previous height? Or should we think base is no longer a dimension, and now we must say that a triangle has length and width, but not base and height?” The child’s questions are legitimate. It’s Jane’s definition of all 3-D shapes having a third dimension of height that’s problematic. Apparently Jane rank ordered length, width, and height and saved the last word, height, for her “third” dimension. But she ran into trouble when she had a 2-D triangle that already has a “height.” First of all, “two-dimensional” and “three-dimensional” are just different aspects of things we perceive or describe. This isn’t like the case where people first invented the clock to tell time and later added a special feature of “alarm” for waking someone up. It’s difficult to imagine the initial invention of an alarm clock without a regular clock having been there already. In this sense, we may say that an alarm clock is a regular clock with an additional feature of alarms...
eBook - ePub- Christine Hopkins, Ann Pope, Sandy Pepperell(Authors)
- 2013(Publication Date)
- David Fulton Publishers(Publisher)
...It is also not uncommon for children to use the names for plane shapes when describing 3-D objects (e.g. square instead of cube, and rectangle instead of cuboid). 3-D objects have faces, vertices and edges. We do not use the word side when describing 3-D shapes as it can be confusing. (We often use sides in 2-D when we mean the outer edge of a polygon; in 3-D the outside is made up of surfaces.) In mathematics a face is any surface of the 3-D object, an edge is where two faces meet, and a vertex (plural vertices) is a point where edges meet. A solid with plane (or flat) faces only A solid with a curved face and two plane faces Think about 3-D shapes you know. Can you think of a shape that has no edges or vertices? A shape that has no vertices? How many edges does it have? Can you think of a shape that has just one edge? A sphere has just one curved face, with no edges or vertices. If you cut through the centre of a sphere you will get a hemisphere – one flat face, one curved face and just one edge. A cylinder has one curved face, two plane faces which are circles and two edges. A cone has one vertex, one edge, a curved face and a flat face. In general an edge is formed wherever two faces meet. POLYHEDRA Polyhedra are 3-D shapes that have flat or plane faces only; this means that the faces are polygons. Cubes and cuboids are everyday examples, as are prisms and pyramids. Cardboard shapes and materials like Polydron or Clixi are excellent for exploring polyhedra. The naming for polyhedra is similar to that for polygons. ‘Poly’ means many and ‘hedron’ means surface (or literally seat). Look at the vertex of a polyhedron...
eBook - ePub- P.K. Jayasree, K Balan, V Rani(Authors)
- 2021(Publication Date)
- CRC Press(Publisher)
...i.e., it deals with measurement of various parameters of geometric figures. It is all about the method of quantifying. It is done using geometric computations and algebraic equations to deliver data related to depth, width, length, area, or volume of a given entity. However, the measurement results got using mensuration are mere approximations. Hence actual physical measurements are always considered to be accurate. There are two types of geometric shapes: (1) 2D and (2) 3D. 2D regular shapes have a surface area and are categorized as circle, triangle, square, rectangle, parallelogram, rhombus, and trapezium. 3D shapes have surface area as well as volume. They are cube, rectangular prism (cuboid), cylinder, cone, sphere, hemisphere, prism, and pyramid. 3.2.1 Mensuration of Areas 3.2.1.1 Circle For a circle of diameter d as shown in Figure 3.1 having circumference C, Area, A = 1 4 π d 2 (3.1a) = π r 2 (3.1b) = 0.07958 C 2 (3.1c) = 1 4 C × d (3.1d) Circumference, C = π d (3.2a) = 3.5449 area (3.2b) Side of a square with the. same area, A = 0.8862 d (3.3a) = 0.285 C (3.3b) Side of an inscribed square = 0.707 d (3.4a) = 0.225 C (3.4b) Side of an inscribed equilateral triangle = 0.86 d (3.5) Side of a square of equal periphery as a circle = 0.785 d (3.6) 3.2.1.2 Square Area = side 2 = 1.2732 × area of inscribed circle (3.7) Diagonal = √ 2 × side (3.8) Circumference of a circle circumscribing a square = 4.443 × side of square (3.9) Diameter of a...
eBook - ePubThe Learning and Teaching of Geometry in Secondary Schools
A Modeling Perspective
- Pat Herbst, Taro Fujita, Stefan Halverscheid, Michael Weiss(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
...p.48 2 GEOMETRIC FIGURES AND THEIR REPRESENTATIONS 2.1. Introduction The notion of geometric figure, while defined loosely as well as restrictedly by Euclid (“14. A figure is that which is contained by any boundary or boundaries”, Euclid, 1956, p. 153), is central to Euclid’s Elements : Postulates enable possible figure constructions, and propositions assert properties of those figures or demonstrate that other figures can be constructed. Later expositions of geometric knowledge have varied in the extent to which they center on the notion of figure, with modern treatises either making figure a centerpiece as an application of set theory (“by figure we mean a set of points”, Moise, 1974, p. 37) or making figure a derived notion within a more general consideration of geometry as the study of transformations of space onto itself (see for example Guggenheimer, 1967; see also Jones, 2002; Usiskin, 1974). The notion of figure has also played a crucial role in scholarship on the teaching and learning of geometry (e.g., Duval, 1995; Fischbein, 1993). This chapter considers how scholarship from various disciplines has influenced our community’s thinking about geometric figures. It brings perspectives from mathematics and mathematicians, from the history and philosophy of mathematics, from cognitive science and semiotics, from technology and from mathematics education proper. Influenced by those perspectives we elaborate on the role of the geometric figure in geometry teaching and learning. We articulate some conceptions of figure related to its various representations in the context of making a curricular proposal on which to found research and development: To conceptualize the study of geometry in secondary schools as a process of coming to know figures as mathematical models of the experiential world...
