 Hi and welcome to the session. Let us discuss the following question. Question says, a phase, the cap used by the turks, is shaped like a frustum of a cone. If its radius on the open site is 10 centimeters, radius at the upper base is 4 centimeters and its slant height is 15 centimeters, find the area of the material used for making it. This is the given figure, 13.24. First of all, let us understand that curved surface area of a frustum of a cone is equal to pi multiplied by L multiplied by r1 plus r2, where L is the slant height of the frustum and r1 and r2 are radii of two circular ends of the frustum. We will use this formula as our key idea to solve the given question. Let us now start the solution. We are given that radius of the cap shaped like frustum on the open site is equal to 10 centimeters. Now we know this side of the cap is open, so radius of the circular end that is r1 is equal to 10 centimeters. And we are also given that radius of the cap on the upper base is equal to 4 centimeters. So let us assume that radius of the cap on the upper base is equal to r2 and r2 is equal to 4 centimeters. So we can write radius of the cap on the open site is equal to r1 is equal to 10 centimeters and radius of the cap on the upper base is equal to r2 is equal to 4 centimeters. We are also given that slant height of the frustum that is L is equal to 15 centimeters. So we can write slant height of frustum is equal to L is equal to 15 centimeters. Now from key idea we know curved surface area of frustum of cone is equal to pi multiplied by L multiplied by r1 plus r2. Where L is the slant height of the frustum r1 and r2 are radii of two circular ends. Now we will substitute corresponding values of L r1 and r2 in this expression. Now we get pi multiplied by 15 multiplied by 10 plus 4 centimeters square. Now substituting 22 upon 7 for pi we get 22 upon 7 multiplied by 15 multiplied by 14 centimeters square. We know 10 plus 4 is equal to 14. Now we will cancel common factor 7 from numerator and denominator both and we get curved surface area of frustum is equal to 660 centimeters square. By multiplying these three terms we get 660 centimeters square. Now we know curved surface area of the frustum does not includes area of these two circular ends and we are given that the cap is closed at one end. So we will add area of this circular end in curved surface area of the frustum and we get total area of the material used for making the cap. Now we will find out area of this circle. We know area of circle is equal to pi r square where r is the radius of the circle. Now area of upper circular base of the cap is equal to pi r2 square. Now substituting corresponding value of r2 and pi in this formula we get 22 upon 7 multiplied by square of 4 centimeters square. This is further equal to 352 upon 7 centimeters square. Now we will find area of material used for making the cap. We know it is equal to curved surface area of frustum plus area of upper circular base. Now substituting corresponding values of these two areas in this expression we get 660 plus 352 upon 7 centimeters square is equal to area of material used for making the cap. Now adding these two terms by taking their LCM we get 4620 plus 352 upon 7 centimeters square. Now this is further equal to 4972 upon 7 centimeters square. Now this is further equal to 7102 upon 7 centimeters square. So we get the area of material used for making the cap is equal to 7102 upon 7 centimeters square. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.