MENSURATION-III

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Kathryn Gilbert
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1 MENSURATION-III CIRCLE: A cicle is a geometical figue consisting of all those points in a plane which ae at a given distance fom a fixed point in the same plane. The fixed point is called the cente and the constant distance is known as the adius. O A cicle with cente O and adius is geneally denoted by C (O, ) CHORD OF CIRCLE: A line segment joining any two points on a cicle is called a chod of the cicle. DIAMETER: A chod passing though the cente of a cicle is known as its diamete. Diamete of a cicle is twice its adius. CONCENTRIC CIRCLES: Cicles having the same cente but with diffeent adii ae said to be concentic cicles. CIRCUMFERENCE: The peimete of a cicle is called its Cicumfeence. The atio of the Cicumfeence (C) of a cicle and its diamete (D) is always constant, which is π. C = π D C = πd = π AREA OF A CIRCLE: The Aea (A) of a cicle of adius () is given by A = π PROBLEMS. The side of a squae is 5 cm which is 3 cm, less than the diamete of a cicle. What is the appoximate aea of the cicle? ) 45 sq cm ) 35 sq cm 3) 65 sq cm 4) 55 sq cm 5) 5 sq cm Diamete (D) of cicle = = 8 cm π D Aea of cicle (A) = = = sq cm 4 4

2 . The diamete of a cicle is 05 cm less than the cicumfeence. What is the diamete of the cicle? ) 4 cm ) 44 cm 3) 48 cm 4) 49 cm 5) None of If D be the diamete of the cicle then its cicumfeence is π D π D D = 05 D = D = = The total aea of a cicle and a squae is equal to 6 sq cm. The diamete of the cicle is 4 cm. What is the sum of the cicumfeence of the cicle and the peimete of the squae? ) cm ) 380 cm 3) 80 cm 4) Cannot be detemined 5) None of ANSWER: Diamete of cicle = 4 cm Its aea = 4 = 386 sq cm 4 Aea of squae = = 5 Side of squae = 5 = 35 Cicumfeence of cicle = 4= 3 Peimete of squae = 4 35 = 40 Requied total = = 4. The aea of a cicle is 54 sq cm. What is the cicumfeence of a cicle? ) 8 cm ) 44 cm 3) 88 cm 4) 08 cm 5) None of ANSWER: If C and A ae cicumfeence and aea of the cicle, then C = 4 A C = 4 54 = 4 = C = = = 44 cm 5. The adius of a cicle is cm less than half the side of a squae whose aea is 56 sq cm. What is the aea of the cicle? ) 3 sq cm ) 54 sq cm 3) 44 sq cm 4) 65 sq cm 5) None of ANSWER: Aea of squae = 56 Side of squae = 56 = 6 6 Radius of cicle (R) = =

3 Aea of cicle = = 54 sq cm 6. The aea of a cicula plot is twice the aea of a ectangula plot. If the aea of the ectangula plot is 088 sq m, what is the peimete of the cicula plot ) 484 m ) 5 m 3) 58 m 4) 440 m 5) None of Aea of cicula plot (A) = 088 = C = 4 6 C = = 4 44 = = 58. The cicumfeence of a cicle is equal to the peimete of a squae. The side of the squae is 33 cm. What is double the diamete of the cicle? ) 4 cm ) cm 3) 0.5 cm 4) 94 cm 5) None of ANSWER: 5 Side of squae = 33 Its peimete = 33 4 = 3 Cicumfeence (C) = D = 3 3 D = = 4 D = 4 = If the cicumfeence of a cicle is deceased by 50%, then the pecentage of decease in its aea is ) 5 ) 50 3) 60 4) 5 5) None of If the cicumfeence deceases by 50% then its adius also deceases by 50%. New adius = Oiginal adius New aea = Oiginal aea = Oiginal aea 4 3 Aea deceased = = = 5% The sum of the cicumfeence of a cicle and the peimete of a squae is equal to cm. The diamete of the cicle is 56 cm. What is the sum of the aea of the cicle and the aea of the squae? ) 464 sq cm ) 644 sq cm 3) 3040 sq cm 4) Cannot be detemined 5) None of Diamete of cicle = 56 cm Its cicumfeence = 56 = 6 cm Peimete of squae = 6 = 96 cm

4 96 Side of squae = = 4 cm 4 56 Aea of cicle + Aea of squae = + 4 = = = The adius of cicle A is twice that of cicle B and the adius of cicle B is twice that of cicle C. Thei aea will be in the atio ) 6 : 4 : ) 4 : : 3) : : 4 4) : 4 : 6 5) None of ANSWER: Radius of C be, then adius of B will be and Radius of A will be 4. Aea of C = π ( ) = π Aea of B = π () = 4π Aea of A = π (4) = 6π Requied atio = 6 π : 4π : π = 6 : 4 :. The cost of building a fence aound a cicula field is ` 4 pe foot. What is the aea of the cicula field? ) sq ft ) sq ft 3) sq ft 4) Cannot be detemined 5) None of ANSWER: Cost of fencing = cicumfeence unit cost 00 = C 4 00 C = = C Aea of cicle A = = 4π = 5 5 = 485 = Thee ae two cicles of diffeent adii. The aea of a squae is 96 sq cm whose side is half the adius of the lage cicle. The adius of the smalle cicle is theeseventh that of the lage cicle. What is the cicumfeence of the smalle cicle? ) π cm ) 6 π cm 3) 4 π cm 4) 3 π cm 5) None of Aea of squae = 96 Side of squae = 96 = 4 Radius of lage cicle = 4 = 8 3 Radius of smalle cicle = 8= Cicumfeence of smalle cicle = π = 4π 3. A cicula oad uns ound a cicula gound. If the diffeence between the cicumfeence of the oute cicle and inne cicle is 44 m, find the width of oad.

5 ) 8 m ) m 3) m 4) 9 m 5) None of ANSWER: R W If R and be the adii of the oute and inne cicle espectively. Then width of the oad = W = (R ) Also π(r ) = (R ) = = = π 44

Lesson-7 AREAS RELATED TO CIRCLES

Lesson-7 AREAS RELATED TO CIRCLES Lesson- RES RELTE T IRLES Intoduction cicle is a plane figue bounded by one line () such that the distance of this line fom a fixed point within it (point ), emains constant thoughout That is constant.