PowerPoint Presentation: WELCOME
THIS PRESENTATION IS MADE BY KAJAL RIMMY PARAMPREET : THIS PRESENTATION IS MADE BY KAJAL RIMMY PARAMPREET
: VISUALISING SOLID SHAPES
INTRODUCTION: INTRODUCTION Plane shapes have two measurements like length and breadth and therefore they are called two-dimensional shapes whereas a solid object has three measurements like length ,breadth and height or depth . Hence they are called three dimensional shapes. Two-dimensional and three-dimensional figure can also be named as 2-d and 3-d. Triangle ,rectangle etc….are 2-d figures. Cube ,cylinder etc are 3-d figures.
2 DIMENSIONAL FIGURES : 2 DIMENSIONAL FIGURES PLANE FIGURES Plane figure have 2 dimension like length and breadth or radius . These figures are called 2 dimensional figures or 2-D. EXAMPLE Rectangle ,circle , square and triangle
SOME EXAMPLES OF PLANE FIGURES: SOME EXAMPLES OF PLANE FIGURES CIRCLE RECTANGLE TRIANGLE SQUARE z
3 DIMENSIONAL FIGURES: 3 DIMENSIONAL FIGURES SOLID OBJECTS A solid object having 3 dimensions like length , breadth , height [depth or thickness] is called 3 dimensional object or 3 – d figure. Example Cube , cuboids , cylinder and cone
SOME EXAMPLES OF SOLID OBJECTS: SOME EXAMPLES OF SOLID OBJECTS
WHAT IS CUBE ?: WHAT IS CUBE ? A cuboid whose length , breadth and height are equal is called a cube. example Sugar cube and dice are example of cube.
SOME EXAMPLES OF CUBE: SOME EXAMPLES OF CUBE
WHAT IS CUBOID ?: WHAT IS CUBOID ? A cuboid has length , breadth and height and its opposite faces are identical . EXAMPLE A wooden box and a matchbox are some example.
SOME EXAMPLES OF CUBOID: SOME EXAMPLES OF CUBOID
WHAT IS SPHERE ?: WHAT IS SPHERE ? A sphere has a curved surface . It Has no vertex and no edge. An object which is in the shape of a ball is said to have a shape of a sphere.
SOME EXAMPLES OF SPHERE: SOME EXAMPLES OF SPHERE
WHAT IS CONE ?: WHAT IS CONE ? A cone has a plane circular end as the base and a curved surface tapering into a point , called its vertex . Thus , a cone has one plane face and one curved face . It has one circular edge and one vertex. EXAMPLE An ice-cream cone and clown’s cap.
SOME EXAMPLES OF CONE: SOME EXAMPLES OF CONE
WHAT IS CYLINDER?: WHAT IS CYLINDER? A cylinder has a curved lateral surface and two circular faces at its end. It has no corner or vertex. A cylinder has two plane faces , namely the top and the base , and one curved face . It has two circular edges. EXAMPLE A circular pipe and gas cylinder.
SOME EXAMPLES OF CYLINDER: SOME EXAMPLES OF CYLINDER
VIEWS OF 3 - D SHAPES: VIEWS OF 3 - D SHAPES 3-Dimensional objects can look differently from different positions so they can be drawn from different perspectives.
DIFFERENT VIEWS OF OBJECTS A PYRAMID FRONT VIEW TOP VIEW SIDE VIEW : DIFFERENT VIEWS OF OBJECTS A PYRAMID FRONT VIEW TOP VIEW SIDE VIEW
WE CAN ALSO GET DIFFERENT VIEWS OF FIGURES MADE BY JOINING CUBES. 1. FRONT VIEW TOP VIEW SIDE VIEW : WE CAN ALSO GET DIFFERENT VIEWS OF FIGURES MADE BY JOINING CUBES. 1. FRONT VIEW TOP VIEW SIDE VIEW
2. TOP VIEW FRONT VIEW SIDE VIEW : 2. TOP VIEW FRONT VIEW SIDE VIEW
FACES , EDGES AND VERTICES: FACES , EDGES AND VERTICES Faces Each of solid is made up of polygonal regions which are called its faces . Edges When any two faces of the solid meet together we get a line segment called an edge.
: Vertex When three or more faces meet at one point , that point is called a vertex. FRONT VIEW
FACES , EDGES AND VERTICES OF CUBE: FACES , EDGES AND VERTICES OF CUBE A cube has 8 vertices , 12 edges and 6 faces.
FACES , EDGES AND VERTICES OF CUBOID: A cuboids has 6 faces , 8 vertices and 12 edges FACES , EDGES AND VERTICES OF CUBOID
FACES , EDGES AND VERTICES OF RECTANGULAR PYRAMID : FACES , EDGES AND VERTICES OF RECTANGULAR PYRAMID A Rectangular pyramid has 5 faces , 8 edges and 5 vertices.
FACES , EDGES AND VERTICES OF triangular pyramid : FACES , EDGES AND VERTICES OF triangular pyramid A triangular pyramid has 4 faces , 6 edges and 4 vertices.
NET FOR BUILDING 3-D SHAPES: NET FOR BUILDING 3-D SHAPES A net is a sort of skeleton -outline in 2-D , which , one folded results in a 3-D shape. Here is a net of cube.
NETS OF CUBE: NETS OF CUBE
NETs OF CUBOID: NETs OF CUBOID
NET OF SQUARE BASED PYRAMID: NET OF SQUARE BASED PYRAMID
DIFFERENT TYPES OF NET : DIFFERENT TYPES OF NET
POLYGONS: POLYGONS A simple closed curve made up of only line segments is called a polygon. EXAMPLES Triangle , square ,octagon ,hexagon , rectangle, pentagon , etc.
DIFFERENT TYPES OF POLYGONS : DIFFERENT TYPES OF POLYGONS SQUARE RECTANGLE TRIANGLE
PENTAGON HEXAGON HEPTAGON: PENTAGON HEXAGON HEPTAGON
OCTAGON NONAGON DECAGON : OCTAGON NONAGON DECAGON
POLYHEDRONS: POLYHEDRONS A polyhedron is a solid shape bounded by polygons EXAMPLE Cubes, cuboids, prisms, and pyramids are few examples of polyhedrons.
NON – POLYHEDRONS : NON – POLYHEDRONS Non-polyhedrons do not have polygon shaped faces. EXAMPLE Spheres, cones and cylinders are a few examples of non-polyhedrons.
CONVEX AND NON-CONVEX POLYHEDRONS : CONVEX AND NON-CONVEX POLYHEDRONS In a convex polyhedron, the line segment joining any two points on the surface of the polyhedron lies entirely inside or on the polyhedron. A polyhedron some of whose plane sections are concave polygons is known as a concave polyhedron.
Concave polygons have at least one interior angle greater than 180° and has some of its sides bent inward. : Concave polygons have at least one interior angle greater than 180° and has some of its sides bent inward.
REGULAR AND IRREGULAR POLYHEDRONS: REGULAR AND IRREGULAR POLYHEDRONS A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.
An irregular polyhedron is made of polygons whose sides and angles are not of equal measure. : An irregular polyhedron is made of polygons whose sides and angles are not of equal measure.
EULER’S FORMULA : EULER’S FORMULA F+V-E =2 ,i.e. , F+V=E+2 is known as Euler’s formula and it holds true for any polyhedron. Here F stands for faces, V for vertices and E for the edges of the polyhedron.
VERIFY EULER’S FORMULA FOR CUBE -:: VERIFY EULER’S FORMULA FOR CUBE -:
SOL. FACES – 6 VERTICES -8 EDGES - 12 = F+V-E=2 LHS= 6+8-12=2 RHS=2 Therefore, LHS=RHS: SOL. FACES – 6 VERTICES -8 EDGES - 12 = F+V-E=2 LHS= 6+8-12=2 RHS=2 Therefore, LHS=RHS
EXERCISE: EXERCISE Choose the correct answer- 1.A cuboid has Length only Length & breadth only Length , breadth & height Thickness only ANSWER – C)
ANSWER- B): ANSWER- B) 2. a gas pipe is an example of a) cube b) cylinder c) Cone d) Cuboid
ANSWER-C): ANSWER-C) 3. a football is an example of a) cylinder b) cone c) sphere d)none of these
Fill in the blanks: Fill in the blanks 4 . The ......faces of a cuboid are identical . ANSWER- OPPOSITE 5 . A...... Has no vertex & no edge. ANSWER- SPHERE
THANK YOU: THANK YOU