 Hello and welcome to the session. The question says the diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground find the area of the playground in meter square. So let's begin with the solution and here in this question diameter and length of the roller is given and it is also given that the roller will take 500 complete revolutions to level the ground and we have to find the area of the playground. First for solving this problem we know that one complete revolution of the roller is equal to the curved surface area of the roller. So for finding the area of the playground we have to multiply the curved surface area of the roller in one complete revolution by 500. Since the curved surface area of the roller is equal to the curved surface area of the cylinder since the roller is in the shape of a cylinder. So this is equal to 2 pi r h where r is the radius and that is equal to 84 upon 2 that is diameter upon 2 since the diameter is 84 cm therefore radius is equal to 42 cm and here h which is the height of the cylinder in this case we are given the length since this is the cylinder we have. So here in this case the height is considered as length of the cylinder and it is denoted by h that is equal to 120 cm right. Now let us find the curved surface area of the roller. So this is equal to 2 into pi into r into h. Now substituting the values of pi r and h we have 2 into 42 into h is 120 into pi. Now we have to assume pi is 22 upon 7 so this can further be written as 2 into 42 into 120 into 22 upon 7 and we are given in the beginning of the exercise that we have to assume pi is 22 by 7 and on simplifying this we have 31680 cm square. So this is the curved surface area of the roller. Now this implies that area covered by the roller in one revolution is equal to 31680 cm square and therefore area covered by the roller in 500 revolutions is equal to 500 into 31680 cm square and this is further equal to 158400 cm square and since 1 cm is equal to 1 upon 100 meters therefore 1 cm square is equal to 1 upon 10000 meter square and thus the area covered in 500 revolutions is equal to 15840000 upon 10000 meter square. So this is equal to 1584 meter square and this is equal to the area of the playground. Hence we are given that it takes 500 complete revolutions to move once over to level the playground hence its area is equal to the area covered by the roller in 500 revolutions that is equal to 1584 meters square. So this is our answer. Hope you have learned it. Take care and have a good day.