 Hello and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, A, B and C, D are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O. If angle A O V is equal to 30 degrees, find the area of the shaded region. This is the given figure 12.32. First of all, let us understand that area of sector of a circle is equal to theta upon 360 multiplied by pi r square. Here, r is the radius of the circle and theta is the angle of the sector in degrees. Now we will use this formula as our key idea to solve the given question. Let us now start with the solution. Now we are given that A, B and C, D are arcs of two concentric circles having common centre O and radius of the outer circle is 21 cm and radius of inner circle is 7 cm and angle theta that is angle subtended by both the arcs C, D and A, B at the centre of the circle is equal to 30 degrees. Area of this shaded region below area of shaded region is equal to area of sector O, A, B minus area of sector O, C, D. So first of all, we will find out area of sector is equal to theta upon 360 multiplied by pi r square. Area of sector O, A, B is equal to 30 upon 360 multiplied by pi multiplied by square of 21 below. Here, theta is equal to radius of the outer circle is equal to 21 cm. So area of sector O, A, B is equal to 30 upon 360 multiplied by pi multiplied by square of 21. Now we will substitute value of pi here. So area of sector O, A, B is equal to 30 upon 360 multiplied by 22 upon 7 multiplied by 21 multiplied by 21 cm square. Now 0 will get cancelled from new return and denominator. You know 7 multiplied by 3 is equal to 21. So we will cancel common factor 7. Now 3 multiplied by 12 is equal to 36. Here, you know 3 multiplied by 4 is equal to 12. Also 2 multiplied by 2 is equal to 4 and 2 multiplied by 11 is equal to 22. Now we get 2 3 1 upon 2 cm square is equal to area of sector O, A, B. Area of sector O is equal to 30 upon 360 multiplied by pi multiplied by square of 7 cm square. Clearly we can see in this sector radius is equal to 7 cm and theta is equal to 30 degrees. So substituting corresponding values of theta and r in formula of area of sector we get this expression. Now substituting value of pi that is 22 upon 7 in this expression we get area of sector O, C, D is equal to 30 upon 360 multiplied by 22 upon 7 multiplied by 7 multiplied by 7 cm square. 0 and 0 will get cancelled. 7 will get cancelled by 7. We know 3 multiplied by 12 is equal to 36. Now 2 multiplied by 6 is equal to 12 and 2 multiplied by 11 is equal to 22. Now simplifying we get 77 upon 6 cm square is equal to area of sector O, C, D. Now we know area of this shaded region is equal to area of sector O, A, B minus area of sector O, C, D. So we can write area of shaded region is equal to area of sector O, A, B minus area of sector O, C, D. Now substituting corresponding values of area of sector O, A, B and area of sector O, C, D in this expression we get area of shaded region is equal to 231 upon 2 minus 77 upon 6 cm square. Now simplifying we get 693 minus 77 upon 6 cm square. Now subtracting these two terms we get 616 upon 6 cm square. Now we will cancel common factor 2 from numerator and denominator both and we get 308 upon 3 cm square is equal to area of shaded region. So clearly we can see area of this shaded region is equal to 308 upon 3 cm square. This is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.