 Hello and welcome to the session. In this session we will discuss a question which says that the slant height of a frustum of a cone is 4 cm and the parameters i.e. circumference of the circular ends are 18 cm and 6 cm. Find the cone surface area of the frustum and use i is equal to 22 by 7 and the options are a 40 cm square, b 34 cm square, c 38 cm square and d 52 cm square. Now before starting the solution of this question we should know some of the results. First is the curve surface area of the frustum of the cone is equal to into i 1 plus i 2 the hole into l where i 1 and i 2 are the radii of the ends of the frustum of the cone and l is the slant height of the frustum of the cone and pi is a constant also r 1 is greater than r 2. Secondly parameter of circumference of a circle is equal to 2 pi r where r is the radius of the circle and pi is now these results will work out as a key idea for solving out this question and now we will start with the solution. Now in the question the parameters of the circular ends of the frustum of the cone are given to us as 18 cm and 6 cm. Now given the perimeter of one circular end is equal to 18 cm and the perimeter of the other circular end of the frustum of the cone is equal to 6 cm. Now we will start the radius of one circular end of the frustum of the cone is equal to r 1. Now using this formula which is given in the key idea so where the perimeter of one circular end of the frustum of the cone with radius r 1 is equal to 2 pi r 1. Now using this value here this implies 18 cm is equal to 2 pi r 1 which further implies 18 cm is equal to 2 into 22 pi 7 into r 1 which further implies r 1 is equal to 18 into 7 over 2 into 22 cm which implies r 1 is equal to here 2 into 9 it will be 63 by 22 cm. Now let the radius of the other circular the perimeter be equal to 2 pi r. Now this is the perimeter of other circular end this implies 6 cm is equal to 2 pi r 2 which implies 6 cm is equal to 2 into 22 pi 7 into r 2 which further implies r 2 is equal to over 2 into 22 cm which implies r 2 is equal to now here 2 into 3 is 6 so it will be 20 over 22 cm. Now the slant height of the frustum of the cone is 4 cm and we have to find the curved surface area of the frustum and when we use this formula to find out the curved surface area of the frustum now given the slant height is equal to 4 cm therefore cut into r 1 plus r 2 the hole into l r 1 this is r 2 and this is l all these values here this will be equal to pi this is 22 plus 7 into 22 plus 21 by 22 the hole into 4 cm square which is further equal to 22 by 7 into on technical IOCM it will be 63 by 21 by 22 which is 84 by 22 into 4 cm square. Now here 7 into 12 is 84 22 will be cancelled with 22 so it will be 38 cm square is 48 cm square and this question is option C which is 48 cm square solution of the given question and that's all for the session hope you all have enjoyed the session.