 Hello and welcome to the session. Here we will discuss the following question which says in the figure that is this figure The boundary of the shaded region consists of four semicircular arcs, two smallest being equal If the diameter of the largest is 14 centimeters and that of the smallest is 3.5 centimeters Calculate the area of the shaded region, use pi is equal to 22 by 7 Now the first having the solution of this question we should know a result And that is, any of the semicircle is 1.2 into pi r square Where i is the radius of the circle and pi is a constant Now this result will work out as a t-idea for solving out this question And now we will start with the solution Now here in this diagram let this be the semicircle 1, this be the semicircle 2 And this be the semicircle 3 and this be the semicircle 4 Now given the diameter of the largest semicircle that is semicircle 1 is 14 centimeters Therefore the radius r1 of semicircle 1 will be equal to 14 by 2 which is equal to 7 centimeters Now using the formula which is given in the t-idea, area of the semicircle is 1 by 2 into pi r square Now the area of semicircle 1 is equal to 1 by 2 into pi r1 square Which is equal to 1 by 2 into pi which is 22 by 7 into r1 square And r1 is 7 centimeters so it will be 7 into 7 centimeters square Which is further equal to, now 2 into 11 is 22, 7 is cancelled with 7 so it will be 77 centimeters square So given that the diameter of the smallest semicircle is 3.5 centimeters So 4 are the smallest semicircles 0.5 centimeters Radius pi which is the diameter over 2 into 35 over 20 which is equal to 7 by 4 centimeters Now the area of into pi which will be equal to 1 by 2 into 22 by 7 into r3 which is equal to 7 by 4 centimeters So where it will be 7 by 4 into 7 by 4 centimeters square Which is further equal to, now 2 into 11 is 22 and 7 is cancelled with 7 so it will be 77 by 16 centimeters square Now the semicircle 3 and semicircle 4 are equal Therefore area of semicircle 3 is equal to semicircle 4 is equal to 77 by 16 centimeters square The area of the shaded portion we want to find the area of the semicircle 2 And far less the radius of the semicircle 2 is required And first of all we will find out the diameter semicircle circle 1 minus semicircle diameter semicircle 1 is 14 centimeters And the diameter of semicircle 3 and 4 is 3.5 centimeters 2 centimeters minus 3.5 centimeters minus 3.5 centimeters Which is equal to 14 centimeters minus 7 centimeters which is further equal to 7 centimeters The diameter is equal to 7 centimeters which implies radius r2 of the semicircle 2 is equal to diameter by 2 which is 7 by 2 centimeters Now semicircle is equal to 1 by 2 into pi which is further equal to 1 by 2 into 22 by 7 into r2 square and r2 is 7 by 2 centimeters So it will be 7 by 2 into 7 by 2 centimeters square Now here 2 into 11 is 22 7 will be cancelled with 7 so it will be equal to 77 by 4 centimeters square Now from the diagram the area of the shaded region will be equal to area of the semicircle 1 plus area of the semicircle 2 minus area of the semicircle 3 minus area of the semicircle 4 So we have the shaded region is equal to area of semicircle plus area of the semicircle 2 minus area of the semicircle Now this is the area of the semicircle 1. This is the area of the semicircle 3 So putting all these values here this implies the shaded region is equal to 77 centimeters square plus 77 by 4 centimeters square minus 77 by 16 centimeters square Which is equal to now taking 77 common within brackets it will be 1 plus 1 by 4 minus 1 by 16 minus 1 by 16 centimeters square Which is further equal to 77 and within brackets on taking the area which is 16 in the numerator it will be 16 plus 4 minus 1 minus 1 centimeters square Which is further equal to 77 into centimeters square Now here 2 into 9 is 18 and 2 into 8 is 16 so this is equal to 77 into 9 by 8 centimeters square Which is equal to 693 over 8 centimeters square So we have the shaded region is equal to 693 over 8 centimeters square So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session