 Hello and welcome to the session. In this session, we will discuss a question which says that a milk container is made of matter sheet in the shape of frustum of cone whose volume is 10459 and 3 by 7 centimeter cube. The weight height of its lower and upper circular ends are 8 centimeters and 20 centimeters respectively. Find the cost of matter sheet used in making the container at the weight of rupees 1.40 pi square centimeter and use pi is equal to 22 by 7. Now before starting the solution of this question, we should know some results. First is the volume of the frustum of cone is equal to 1 by 3 into pi into h into r whole square plus r2 square plus r1 into r2 the whole, where r1 and r2 are the radial of the circular ends of the frustum of the cone and also r1 is greater than r2 and h is the height of the frustum of cone and pi is a constant. Secondly, the correct surface area of the frustum of cone is equal to pi into r1 plus r2 the whole into l where l is the slant height of the frustum of the cone and l is also equal to square root of h square plus r1 minus r2 whole square. Now these results will work out as a key idea for solving out this question and now we will start with the solution. Now here it is given a milk container is made of matter sheet in the shape of frustum of cone. Also it is given that the radius of the lower circular end is 8 centimeters and the radius of the upper circular end is 20 centimeters. So given r1 is equal to 20 centimeters which is the radius of the upper circular end and r2 is equal to 8 centimeters which is the radius of the lower circular end. Also the volume of the container is given to us also volume of the container is equal to 10459 and 3 by 7 centimeter cube which is equal to 73216 by 7 centimeter cube. Now using this result which is given in the key idea the volume of the container here will be 1 by 3 into pi into h into r1 square plus r2 square plus r1 into r2 the whole which is equal to 73216 by 7 centimeter cube. Now putting the values of r1 and r2 here this implies 1 by 3 into pi which is 22 by 7 into h into 20 square plus 8 square plus 20 into 8 the whole is equal to 73216 by 7 centimeter cube which further implies 22 by 21 into h into 400 plus 64 plus 160 the whole is equal to 73216 by 7 centimeter cube which further implies 22 by 21 into h into 624 is equal to 73216 by 7 centimeter cube which implies h is equal to 73216 into 21 over 22 into 7 into 624. Now here 7 into 3 is 21 and here 3 into 208 is equal to 624 into 11 is 22 and 2 into 36608 is 73216. Now 11 into 3228 is equal to 6608 and here 28 into 16 is equal to 3328. So h is equal to 16 centimeters. Now using this formula which is given in the key idea slant height that is l is equal to square root of h square plus r1 minus r2 whole square. Now putting the values of r1 r2 and h here this will be equal to square root of 16 square plus 20 minus 8 whole square which is further equal to square root of 256 plus 20 minus 8 is 12 and 12 square is 144. So this will be equal to square root of 400 which is equal to 20 centimeters. Now using the formula which is given in the key idea surface area of the container is equal to curved surface area of the container which is the curved surface area of the frustum of cone plus area of the circular base that is this circular base with radius r2. So this will be equal to pi into r1 plus r to the whole into l which is the curved surface area of frustum of cone plus area of the circular base with radius r2 and that will be pi r2 square. So this is equal to taking pi common it will be pi into r1 plus r to the whole into l plus r to square the whole. Now putting the values of r1 r2 and l here this will be equal to pi is 22 by 7 into 20 plus 8 the whole into 20 plus 8 square the whole which is equal to 22 by 7 into 28 into 20 plus 64 the whole which is formula equal to 22 by 7 into 560 plus 64 the whole which is equal to 22 by 7 into 624 centimeters square. Now we have to find the total cost of metal sheet used in making the container at the rate of rupees 1.40 by square centimeter. So the total cost of metal sheet at the rate of rupees 1.40 per centimeter square is equal to rupees 1.40 into the surface area of the container that is 22 by 7 into 624 which is equal to 2745.60 rupees. So this is the solution of the given question and that's all for this session hope you all have enjoyed the session.