 Hello and welcome to this session. In this session we will discuss solid shapes. First let's see what are two-dimensional and three-dimensional shapes. Plane shapes have two measurements like length and breadth and so these plane shapes are called two-dimensional shapes. Whereas we have that the solid objects have three measurements like length, breadth and height. Or you can say the depth and so these solid objects are called the three-dimensional shapes. This two-dimensional figure is named as 2D and a three-dimensional figure is named as 3D. For example consider this rectangle it has two measurements the length and the breadth and therefore this is a 2D figure. Also square, triangle, circle are other 2D figures. Consider this cuboid it has three measurements length, breadth and the height. So this is a 3D figure. The other 3D figures are cubes, cones, cylinders, spears etc. Since all these figures have three measurements. In our day to day life we come across many objects which are the combinations of different shapes. Like if you consider this figure this is the combination of a cylinder and a cone. That is a cone is surmounted on a cylinder. Next we shall discuss view of 3D shapes. A 3D object or you can say a three-dimensional object looks differently from different positions and so we can draw a 3D object from different perspectives. An object can have three views top view, side view and the front view. Consider this matchbox this is the top of the matchbox this is the front of the matchbox and this is the side of the matchbox. Now we will draw three different views of this matchbox that is we will draw the top view, side view and the front view. So this is the front view of the matchbox this is the side view of the matchbox and this is the top view of the matchbox. So given any object we can draw the top view, side view and the front view of any given object. We can also get different views of the figures which are made by joining the cubes. This is a given solid made up of cubes. This is the top of the solid this is the side and this is the front. Now we shall make or we shall draw the top view, side view and the front view of this given solid. This figure is the top view of the given solid this is the side view of the given solid and this is the front view. Next we discuss mapping space around us. Let's see what is a map. A map depicts the location of a particular object or a place in relation to other objects or places. It is different from a picture and we also say that there is no reference or perspective in a map. Like if you consider the map of the house it would remain the same irrespective of the position of the observer. So we say that perspective is not important or not relevant for a map. Symbols are used to depict different objects or places in a map and also maps use a scale which is fixed for a particular map. Moreover we say that the scale reduces the real distances proportionately to distances on the paper. This is a map which shows the route of Ram's school to his house. These are the different symbols that we have used in the map. This is for the house, this is for the school, this is for the shop, this is for the hotel and this is for the park. And we have also used proper scale like we have mentioned the distances. So this is how we can easily visualize the map. Next we discuss faces, edges and vertices. Solids are made up of polygonal regions which are called its faces. Then edges are the line segments where the faces meet. Then vertices are the points where the edges meet. And such solids which are made up of polygonal regions has faces, edges and vertices are called polyhedrons. Consider this figure, these are the faces of this figure or you can say of this polyhedron. And these line segments are the edges and these are the vertices of the polyhedron. Next we have convex polyhedrons in this no portion of its dinals meet outside the polyhedron. The next is a regular polyhedron. It is a polyhedron in which its faces are made up of regular polygons. The same number of faces meet at each vertex. Like if you consider this polyhedron, this is a convex polyhedron like this figure is a regular polyhedron. Next we discuss about prisms and pyramids which are two very important members of polyhedron family. First let's see what is a prism. A prism is a polyhedron whose base and top are congruent polygons whose other faces that is the lateral faces are parallelogram in shape. Like this figure is a prism. Now let's see what is a pyramid. A pyramid is a polyhedron whose base is a polygon of any number of sides and whose lateral faces are triangles with a common vertex. Like if you consider this figure, this is a pyramid. Next we have Euler's formula. We have for any polyhedron f plus v minus e is equal to 2 where we have f rd, number of faces of a polyhedron, v rd, number of vertices of the polyhedron and e are the number of edges of the polyhedron. Like if we have that the number of faces of a polyhedron is equal to 8, number of vertices that is v is 6 and the number of edges e is 12. Let's verify the Euler's formula. We have f plus v minus e, so this would be equal to 8 plus 6 minus 12 and this is equal to 2. And according to Euler's formula we have f plus v minus e is equal to 2. Let's verify since we got f plus v minus e equal to 2. So this completes the session. Hope you have understood the concept of solid shapes and hope you have understood how we visualize the solid shapes.