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➢The distance covered by travelling once around a, circle is its perimeter, usually called its, circumference. = 2Πr, r= radius, Π = 22/7 or (3.14), , ➢Area of the circle =πr2, , 2, , 11/22/2019
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Qn:The cost of fencing a circular field at the rate of, Rs 24 per metre is Rs 5280. The field is to be, ploughed at the rate of Rs 0.50 per meter square ., Find the cost of ploughing the field (Take π = 22/7 ), , 3, , 11/22/2019
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Areas of Sector and Segment of a Circle, ➢The portion (or part) of the circular region enclosed by two, radii and the corresponding arc is called a sector., ➢The portion (or part) of the circular region enclosed between, a chord and the corresponding arc is called a segment of the, circle., , 5, , 11/22/2019
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(Arc APB), 6, , 11/22/2019
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Area of the segment APB = Area of the sector OAPB–, Area of Δ OAB, , 7, , 11/22/2019
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OR, , 8, , 11/22/2019
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Qn:Find the area of the sector of a circle with, radius 4 cm and of angle 30°. Also, find the area of, the corresponding major sector (Use π = 3.14)., , 10, , 11/22/2019
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Solution, Given sector is OAPB (see Fig)., , 11, , 11/22/2019
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Qn:Find the area of the segment AYB shown in, Fig, if radius of the circle is 21 cm and ∠ AOB =, 120°. (Use π = 22/7 ), , 12, , 11/22/2019
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HW: 1)EXERCISE 12.2 , qn:1, qn:4, , Qn:Find the area of a quadrant of a circle whose, circumference is 22 cm, , 16, , 11/22/2019
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Ans:, , 17, , 11/22/2019
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Qn:The length of the minute hand of a clock is, 14 cm. Find the area swept by the minute, hand in 5 minutes., , 19, , 11/22/2019
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Ans :, , Therefore swept by 5 minutes= 360/12=30 degree, , 20, , 11/22/2019
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Qn:In a circle of radius 21 cm, an arc subtends an, angle of 60° at the centre. Find:, (i) the length of the arc, (ii) area of the sector formed by the arc, (iii)area of the segment formed by the, corresponding chord, , 21, , 11/22/2019
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Ans :, (i), , (ii)area of the sector(OAPB) formed by the arc=, , 22, , 11/22/2019
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(iii)area of the segment formed by the corresponding chord, , 23, , 11/22/2019
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(Base), 24, , 11/22/2019
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Qn:An umbrella has 8 ribs which are equally spaced (see Fig)., Assuming umbrella to be a flat circle of radius 45 cm, find the, area between the two consecutive ribs of the umbrella., , Figure:, 26, , 11/22/2019
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Ans:, , 27, , 11/22/2019
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Qn:Tick the correct answer in the following : Area of a, sector of angle ‘p’ (in degrees) of a circle with radius R is, , Ans:, , 29, , 11/22/2019
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Areas of Combinations of Plane Figures, , Let us now try to calculate the areas of some, combinations of plane figures., EG: 4 circles of diametre 2 cm,vertexes of square placed at, the orgin of the circles ,find the are of shaded region?, , (22/7 x 1)-4= ?, , 30, , 11/22/2019
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Qn: In Fig., two circular flower beds have been, shown on two sides of a square lawn ABCD of, side 56 m. If the centre of each circular flower, bed is the point of intersection O of the, diagonals of the square lawn, find the sum of the, areas of the lawn and the flower beds., , 31, , 11/22/2019
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Ans:, , (, , Ar, , )+, , o, , +, , 32, , +, , 11/22/2019
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Qn:Find the area of the shaded region in Fig, where, ABCD is a square of side 14 cm., , 34, , 11/22/2019
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Ans:, , area of the shaded region = Area of the square ABCD- area, of the four circles, , 35, , 11/22/2019
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Qn:Find the area of the shaded design in Fig. 1,, where ABCD is a square of side 10 cm and, semicircles are drawn with each side of the square, as diameter. (Use π = 3.14), , 37, , 11/22/2019
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Ans:, , 38, , 11/22/2019
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= Area of ABCD – Areas of two semicircles of, each of radius 5 cm, , 39, , 11/22/2019
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Similarly, Area of II + Area of IV = 21.5 cm2, , 40, , 11/22/2019
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Qn:Find the area of the shaded region in, figure, if PQ = 24 cm, PR = 7 cm and O is, the centre of the circle., , 41, , 11/22/2019
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Ans:, Area of shaded region = Area of semicircle – Area of right, triangle RPQ, <RPQ =90 degree ( Angle in semi-circle is 90 degree), , = 49 + 576 = 625, RQ = 25 cm= Diameter of the circle, Radius=25/2, , 42, , 11/22/2019
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Area of the semicircle=, , Area of right triangle RPQ=1, , PQ X PR, , Area of shaded region = Area of semicircle – Area of right, triangle RPQ, =, , 43, , 11/22/2019
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HOME WORK 1: Find the area of the shaded region in, Fig. 12.20, if radii of the two concentric circles with centre, O are 7 cm and 14 cm respectively and ∠ AOC = 40°., , Area of shaded region = Area of sector OAC – Area of sector, OBD, 44, , 11/22/2019
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HOME WORK 2:Find, , the area of the shaded region in, Fig. 12.21, if ABCD is a square of side, 14 cm and APD and BPC are, semicircles., , 45, , 11/22/2019
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Qn:Find the area of the shaded region in Fig, where a, circular arc of radius 6 cm has been drawn with vertex, O of an equilateral triangle OAB of side 12 cm as, centre., , 46, , 11/22/2019
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Ans:, , Radius of the circle = 6 cm, Side of the triangle AOB= 12 cm, 47, , 11/22/2019
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Qn:From each corner of a square of side 4 cm a, quadrant of a circle of radius 1 cm is cut and also a circle, of diameter 2 cm is cut as shown in Fig.. Find the area of, the remaining portion of the square., , 50, , 11/22/2019
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Ans:, , Area of shaded region = Area of square - Area of 4 quadrant-area, of a cirdcle., Area of 4 equal quadrant=area of a 1 circle=, , Then area of 4 quadrant=4 x 11/14, , 51, , 11/22/2019
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Note:Area of 4 equal quadrant = area of a 1 circle=, (Same Radius), Qn:In Fig, OACB is a quadrant of a circle with centre O and, radius 3.5 cm. If OD = 2 cm, find the area of the, (i) quadrant OACB, (ii) shaded region, , 52, , 11/22/2019
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Home work: page No :237 Qn: 13,14 (exc 12.3), 53, , 11/22/2019
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Qn:In Fig, ABC is a quadrant of a circle of radius 14 cm, and a semicircle is drawn with BC as diameter. Find the, area of the shaded region., , 54, , 11/22/2019
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Ans:, , (sector), D, , 55, , 08/12/2019
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Area, , 56, , 11/22/2019
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Qn:In Fig, AB and CD are two diameters of a circle, (with centre O) perpendicular to each other and OD is, the diameter of the smaller circle. If OA = 7 cm, find the, area of the shaded region., , 57, , 11/22/2019
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