PROJECT WORK OF MATHS: PROJECT WORK OF MATHS KENDRIYA VIDYALAYA GINGLE , URI NAME – ATUL TYAGI CLASS -VII ROLLNO. - 10
PowerPoint Presentation: 2) TOPIC - VISUALISING SOLID SHAPES WELCOME
DIMENSIONAL FIGURES : 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 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. FACES , EDGES AND VERTICES
: 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 OF SQUARE BASED PYRAMID: NET OF SQUARE BASED PYRAMID
Surface area and volume of 3-dimensional Figures: Surface area and volume of 3-dimensional Figures
PowerPoint Presentation: Top Right Side Front Bottom Top Front Back Right Side Left Side Cuboid A Cuboid has 6 faces.. Each face is a rectangle . Front
PowerPoint Presentation: face face face Cube is also having 6 faces ( Here three faces are visible ) 1 2 3 Dice (Pasa) cube
Surface area and volume of 3-dimensional Figures: Surface area and volume of 3-dimensional Figures
PowerPoint Presentation: Top Right Side Front Bottom Top Front Back Right Side Left Side Cuboid A Cuboid has 6 faces.. Each face is a rectangle . Front
PowerPoint Presentation: face face face Cube is also having 6 faces ( Here three faces are visible ) 1 2 3 Dice (Pasa) cube
PowerPoint Presentation: Surface area = Area of all six faces = 6a 2 a Surface area Cube cuboid Surface area = Area of all six faces = 2(lxb + bxh +hxl) a a a (Here all the faces are square) (Here all the faces are rectangular) h l b
PowerPoint Presentation: Area of base (Rectangle) = l x b l Height of cuboid = h Volume of cuboid = Area of base x height = (l x b) x h =lXbXh h Volume of cuboid Front b
PowerPoint Presentation: Volume of Cube a a Area of base (square) = a 2 Height of cube = a Volume of cube = Area of base x height = a 2 x a = a 3 a a
PowerPoint Presentation: 2 π r h r h Curved Surface area of cylinder = Area of rectangle= 2 π rh Method of Finding Curved Surface area of Cylinder r
PowerPoint Presentation: Total Surface Area of a Cylinder = (2 π r) x( h) + 2 π r 2 Curved surface Area of curved surface + area of two circular surfaces circular surfaces = 2 π r( h+ r)
PowerPoint Presentation: Circumference of circle = 2 π r Area covered by cylinder = curved Surface area of of cylinder = (2 π r) x( h) r h Method of finding Curved Surface area of cylinder It is the area covered by the outer surface of a cylinder. Formation of Cylinder by bangles Circumference of circle = 2 π r r
PowerPoint Presentation: Volume of cylinder Volume of cylinder = Area of base x vertical height = π r 2 xh r h
PowerPoint Presentation: Curved Surface Area of Cone Base r h l = Slant height Curved Surface Area of a Cone = π r l where l = √ ( r²+h ² )
PowerPoint Presentation: 3( V ) = π r 2 h r h h r Volume of a Cone Here the vertical height and radius of cylinder & cone are same. 3( volume of cone) = volume of cylinder V = 1/3 π r 2 h
PowerPoint Presentation: If both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone , Volume = 3V Volume =V
PowerPoint Presentation: 4( 1/3 π r 2 h ) = 4( 1/3 π r 3 ) = V h=r r Volume of a Sphere Here the vertical height and radius of cone are same as radius of sphere . 4( volume of cone) = volume of Sphere V = 4/3 π r 3 r
PowerPoint Presentation: Surface area 6a 2 2 π rh π r l 4 π r 2 Volume a 3 π r 2 h 1/3 π r 2 h 4/3 π r 3 Comparison of Area and volume of different geometrical figures
NOW QUESTION TIME: Q1- FOOTBALL IS AN EXAMPLE OF ? NOW QUESTION TIME CUBE CONE SPHERE NONE OF THESE
PowerPoint Presentation: RIGHT ANSWER
PowerPoint Presentation: WRONG ANSWER
PowerPoint Presentation: WHICH OF THESE IS A EXAMPLE OF CUBE PIPE SUN NONE OF THESE DICE
PowerPoint Presentation: RIGHT ANSWER
PowerPoint Presentation: WRONG ANSWER
PowerPoint Presentation: The End