 Hello and welcome to the session I am Deepika here. Let's discuss a question which says in given figure a brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure. Find the total length of the silver wire required to the area of each sector of the brooch. Now this problem is based on the area of a sector of a circle and we know that the area of the sector of angle theta is equal to theta upon 360 into pi r square where r is the radius of the circle theta the angle of the sector in degrees. In this question we will also use the formula of the circumference of a circle. We know that the circumference of a circle equal to 2 pi r. So this is a key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution part 1. We are given a brooch is made with silver wire in the form of a circle with diameter 35 mm that is diameter of brooch is 35 mm therefore radius of brooch is 35 upon 2 mm because we know that radius is equal to half of diameter. Now the wire is also used in making 5 diameters which divide the circle into 10s equal sectors as shown in this figure. Therefore the total length of the silver wire required is equal to circumference of the brooch plus length of 5 diameters. Now brooch is in the form of a circle therefore circumference of the circle is equal to 2 pi r plus length of 5 diameters and this is equal to 2 into take pi is equal to 22 upon 7 into radius is 35 upon 2 mm plus 5 into diameter is 35 mm so 5 into 35 mm this is equal to 110 mm plus 175 mm and this is equal to 285 mm hence the answer for part 1 is the total length of the silver wire required is 285 mm. Let's move to the part 2. In part 2 we have to find the area of each sector of the brooch. Now in a way we can consider this circular region to be a sector forming an angle of 360 degree at the center. Now this circular region is divided into 10 equal sectors therefore the angle of each sector equal to 360 degree upon 10 and this is equal to 36 degree. Now according to our key idea area of the sector of angle theta is equal to theta upon 360 into pi r square. Now here theta is 36 degree so this is equal to 36 upon 360 into take pi is 22 upon 7 into r that is 35 upon 2 mm into 35 upon 2 mm. So on cancellation we have 11 into 35 upon 4 mm square and this is equal to 385 upon 4 mm square. Hence the required answer for part 2 is 385 upon 4 mm square. I hope the solution is clear to you. Bye and take care.