 Hello friends, let's work out the following problem. It says, a bucket made up of a metal sheet is in the form of a frustrum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of the metal sheet used is Rs 15 per 100 cm square. So let's now move on to the solution. We are given that bucket is in the form of a frustrum of a cone. We have to find the cost of the bucket. So if we are able to find out how much metal sheet is used to make that bucket, we can find the cost of the bucket because we know the cost of the metal sheet. So our motive is to find the metal sheet used to make that bucket. That means we have to find the area of the metal sheet right which is in the shape of a frustrum. So this is the bucket which is in the form of a frustrum and the radius, the lower end is given to be 8 cm and the radius upper end is given to be 20 cm and the height bucket is given to be 16 cm. Now we have to find the area of the metal sheet used to make this bucket. So the metal sheet to make is equal to the curve surface area of the bucket, area of the base. Since the bucket is open from the upper end, we just have to find the curve surface area and the area of the lower base. Let us denote the radius of the lower end by r1 and radius of the upper end by r2. Now the formula for the curve surface area of the frustrum pi into L into r1 plus r2 where L is the slant height given by the formula under the root x square plus r1 minus r2 whole square. Here since r2 is the radius of the upper end it should be r2 minus r1 whole square. Now substitute the values of h, r2 and r1 in this formula. So this becomes 16 square plus 20 minus 8 whole square which is equal to under the root 16 square is 256 plus 12 square is 144. This is equal to under the root 400 which is equal to 20. So this slant height is 20 centimeter. Now the curve surface area of the frustrum into 20 into r1 plus r2 is 8 plus 20. So this is equal to pi into 20 into 28. So this is equal to 50 560 pi. Now we have to find the area of the base. Now since the radius of the lower end is 8 centimeter. So the area of the base is pi r1 square because it is in the shape of circle the lower end is in the shape of the circle. So this becomes pi into 8 square. So this is equal to 64 pi. Now we know that the area of the metal sheet required to form the bucket is the curved surface area of the bucket plus area of the base. Now the curved surface area of the bucket is 560 pi and the area of the base is 64 pi. So we have area of the metal sheet required to form the bucket is 560 pi plus 64 pi which is equal to 624 pi centimeter square. The unit of the area is centimeter square. Now we are given that the cost of the metal sheet of area 100 centimeter square is rupees 15. So this implies the cost of the metal sheet of area 1 centimeter square is rupees 15 upon 100. And this implies the cost of the metal sheet of area 624 centimeter square is equal to rupees 15 upon 100. into 624 this is equal to rupees 15 upon 100 into 624 pi is 3.14. Now simplifying this 5355 into 20 is 100. So we have this as rupees 3 upon 20 into 624 into 3.14. Now again this is equal to rupees 3 into 624 into 3.14 is 5878.08 upon 20. And this gets simplified to rupees 293.90. So this is the cost of the metal sheet required to make that bucket. Hence the cost of the bucket equal to rupees 293.90. So this completes the question and the session. Bye for now. Take care. Have a good day.