 Hi and welcome to the session. Today we will learn about visualizing solid objects. Visualizing solid objects is an important and useful skill as sometimes we are given such solid shapes which are the combination of various solid shapes. And when we see such shapes from the front we may not be able to see the hidden parts. For example, here this box is formed by joining three cuboids. By visualizing solid objects we can find the measurements of the given solids. So here if we are given that the measurement of each cuboid is 3 cm by 1 cm by 2 cm then we can easily find out the measurement of the box. Now here length of each cuboid is 3 cm so this will be 3 cm. Again this will be 3 cm and this will also be 3 cm. Thus the length of this whole box will be 3 cm plus 3 cm plus 3 cm which will be 9 cm. Now width of each cuboid is 1 cm so this will be 1 cm which will be same for the box also. So the width of the box is 1 cm and the height of each cuboid is 2 cm. So here this height is 2 cm that means the height of the box will also be 2 cm. Thus the measurement of the box will be 9 cm by 1 cm by 2 cm. Thus here we were able to find the measurements of the box only by visualizing this given solid object. Now next topic is viewing different sections of each solid. One way to view an object is by cutting or slicing. Suppose we have a cylindrical pipe. Now this will be cylindrical in shape. Now the cylindrical pipe will have circular ends on both the sides. So if we cut it vertically then we will get many pieces which will look like circles. Like this and all these pieces that is all these circles will be of same radii as the radii of the cylindrical pipe will be same everywhere. Now these pieces are known as the cross sections of the cylindrical pipe. Thus we have that the cross sections of this cylindrical pipe will be circles. Now if by chance these cuts will not be vertical then you may get different cross sections. Now another way is by shadow plane. For shadow plane we need a source of light and some solid shapes. If we have the overhead projector then we can place the solid under its lamp and we can see the shadow of the solid. If the solid is a 3 dimensional shape then its shadow will be a 2 dimensional shape. For example if we place a cube under the lamp then its shadow will be a square. The shadow of a sphere same amount of orange ball will be a circle. Now if we have an ice cream cone then the shadow of the cone will be a triangle. And if we place any cuboidal box then its shadow will be a rectangle. Here all the solids are 3D shapes and their shadows are 2D shapes. So by using shadow plane 3 dimensional objects can be viewed in 2 dimensions. And now a third way is by looking at an object from certain angles to get different views. If we have a solid then we can look at it from the front, from the side and from the top to get the information about the shape of the solid. Now suppose we are given this solid. Now if we look at it from the front then we will be able to see this is square, this is square, this is square and this is square. So its front view will be like this. Now if we look at it from the top then we will be able to see this is square, this is square and this is square. So its top view will be like this. If we look at it from any of the sides then we will be able to see these 2 squares. So this will be its side view. Thus after gathering all this information we can say that this figure has been formed by joining 4 cubes. So now we have learned 3 ways of looking at a 3 dimensional object. This will help you a lot in your day to day life. With this we finished this session. Hope you must have enjoyed it. Goodbye, take care and have a nice day.