 Hello and welcome to the session. My name is Asha and I shall be helping you with the following problem that says in figure 13.12 you see the frame of a lampshade. It is to be covered with a decorated cloth. The frame has base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and the bottom of the frame. Find how much cloth is required for covering the lampshade. Where we are given the diameter of the lampshade is 20 cm and also we are given the height of the lampshade is 30 cm and we are given that the margin of 2.5 cm is to be given for folding it over the top and bottom so this implies the total height of the cloth required is 30 cm is the height of the cylinder plus 2.5 cm from the bottom and 2.5 cm from the top. So the total height of the cylinder will be 30 plus 2.5 plus 2.5 that is 35 cm. Let us now begin with the solution and here we are given that lampshade is of the shape of a cylinder right and we are given the diameter of the lampshade is equal to 20 cm. So this implies the radius of the lampshade is equal to diameter upon 2 which is equal to 10 cm. Let us denote the radius of the lampshade by r and also we are given that height of the lampshade is equal to 30 cm. Now a margin of 2.5 cm is to be given for folding it over the top and bottom of the frame therefore total height of the lampshade or in other words we can say the length of the cloth required is equal to 30 plus 2.5 plus 2.5 cm right and this is equal to 35 cm since if this is a lampshade suppose right this is a rough figure we are making and this is a height we are given 30 cm and its margin of 2.5 cm so this is the height of 2.5 cm above this is the height of 2.5 cm below and this is the total length of the cloth required to cover it. So it is 30 cm plus 2.5 plus 2.5 and this is equal to 35 cm. Now we have to find the area of the cloth to cover the lampshade so this is equal to curved surface area of the lampshade with radius 10 cm and height 35 cm right so this is equal to the curved surface area of a cylinder is 2 pi r h. Let us denote the length of the cloth required by h so we have 2 into 22 upon 7 radius is 10 cm and height is 35 so this gives 7 pi to 35 and we further have on multiplying it 2200 and since the unit of height and radius is in cm so we have cm square. Thus the area of cloth required to cover the lampshade such that a margin of 2.5 cm is given on the top and the bottom is 2200 cm square so this completes the session by intake care.