 Hi and welcome to the session. Let us discuss the following question. The question says, an ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round? Here A, B and C are the three food pieces. Before proceeding for the solution, let us recall the formula of circumference of circle that is equal to 2 pi R where R is the radius of the circle. So this is the key idea of the question. Now let us see its solution. We need to find that for which food piece would the ant have to take a longer round? Now taking a round means finding out the perimeter of all these shapes. So first of all let us find out the perimeter of shape A. Now for our convenience let us mark the points A and B. So here A, B is a semicircle whose diameter is 2.8 centimeters. So for shape A diameter is equal to 2.8 centimeters. So this implies its radius will be equal to 2.8 upon 2 centimeters that is equal to 1.4 centimeters. Now let us find out the circumference of the semicircle A, B. So circumference of semicircle A, B is equal to, now we know that the circumference of a circle is 2 pi R. So the circumference of semicircle A, B will be 1 by 2 into 2 pi R that is half of circumference of a circle. Now this will be equal to 1 by 2 into 2 into pi is 22 upon 7 into R. R is radius that is 1.4 centimeters. On simplifying this we will get 4.4 centimeters as the circumference of semicircle A, B. Now let us find perimeter of figure A that will be equal to length of A, B plus circumference of the semicircle A, B is equal to, now here length of A, B is 2.8 centimeters plus circumference of semicircle A, B is 4.4 centimeters. So adding them we will get 7.2 centimeters. So distance covered by aunt for food piece A is equal to 7.2 centimeters. Now let us find out the perimeter of the shape B. So for shape B let us mark out the points P, Q, S. So here perimeter will be PQ plus Q1 plus RS plus circumference of the semicircle SP. So here first of all let us find the circumference of the semicircle whose diameter is 2.8 centimeters. So for semicircle PS diameter is equal to 2.8 centimeters. This implies radius will be equal to 2.8 upon 2 centimeters that is equal to 1.4 centimeters and thus the circumference of semicircle PS is equal to 1 by 2 into 2 pi R which is equal to 1 by 2 into 2 into pi S 22 by 7 into R. R is radius that is 1.4 centimeters. On simplifying this we will get 4.4 centimeters. Therefore perimeter of shape V is equal to PQ plus QR plus RS circumference of semicircle PS that is 1.5 centimeters. QR is 2.8 centimeters. RS is 1.5 centimeters. Circumference of the semicircle PS is 4.4 centimeters. Now this is equal to 10.2 centimeters. Therefore distance covered by an ant for food piece B is equal to 10.2 centimeters. Lastly let us find out the perimeter of the shape C. So for shape C let us mark the points M N O. So here the perimeter is M N plus N O plus circumference of the semicircle M O. So first of all let us find out the circumference of the semicircle M O. Here also the diameter is 2.8 centimeters. For semicircle diameter is equal to 2.8 centimeters. This implies radius will be equal to 2.8 upon 2 centimeters that is equal to 1.4 centimeters. Therefore circumference of semicircle M O is equal to 1 by 2 into 2 pi R that is equal to 1 by 2 into 2 into pi is 22 by 7 into R RS 1.4 centimeters. Now simplifying this we will get 4.4 centimeters. So circumference of the semicircle M O is 4.4 centimeters. So perimeter of shape C is equal to M N plus circumference of semicircle M O that is equal to M N that is 2 centimeters plus N O also 2 centimeters plus circumference of semicircle M O that is 4.4 centimeters. So this is equal to 8.4 centimeters. Therefore the distance covered by ant for food piece C is equal to 8.4 centimeters. Now let's see for which food piece the ant has to take the longer round. Here the distance covered by ant for the food piece A is 7.2 centimeters and distance covered by ant for food piece B is 10.2 centimeters and lastly the distance covered by ant for the food piece C is equal to 8.4 centimeters. So the ant travels the most for the food piece B that is 10.2 centimeters. Therefore takes the longest round for the food piece B. Therefore food piece B is the required answer and with this we finish this session. Hope you must have understood the concept. Goodbye and take care.