Subject UNIT 7 THE CIRCUMFERENCE AND AREA OF

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UNIT 7 : THE CIRCUMFERENCE AND AREA OF CIRCLE SUB UNITS : 1) CIRCUMFERENCE OF A CIRCLE 2) RELATION BETWEEN CIRCUMFERENCE AND DIAMETER. 3) VALUE OF Л. 4) AREA OF CIRCLE 5) EXAMPLES

CIRCUMFERENE OF CIRCLE: A WIRE RING IS SHOWN IN THE FIGURE ALONGSIDE. WE CAN BREAK THIS RING AT ANY POINT ON IT, STRAIGHTEN OUT THE WIRE AND MEASURE ITS LENGTH. THIS LENGTH IS CALLED THE CIRCUMFERENCE OF THE CIRCLE.

RELATION BETWEEN CIRCUMFERENCE AND DIAMETER THE RATIO OF THE CIRCUMFERENCE OF ANY CIRCLE TO ITS DIAMETER IS A CONSTANT AND THIS CONSTANT IS AN IRRATIONAL NUMBER. THE GREEK LETTER π IS USED AS A SYMBOL FOR THIS SYMBOL. CIRCUMFERENCE DIAMETER = Л

EXAMPLE 1. A CIRCLE HAS A DIAMETER OF 7 CM. FIND ITS CIRCUMFERENCE. C=πd = (22/7) x 7 =22 cm CIRCUMFERENCE=22 cm.

EXAMPLE 2. A CIRCLE HAS A RADIUS OF 35 CM. FIND ITS CIRCUMFERENCE. C = 2π r =2 x (22/7) x 35 = 220 cm CIRCUMFERENCE = 220 cm.

EXAMPLE 3. THE DIAMETER OF A BULLK-CART WHEEL IS 1. 4 HOW MANY TIMES MUST THE WHEELS ROTATE FOR THE CART TO COVER A DISTANCE OF 1. 1 KM? CIRCUMFERENC OF WHEEL = 1 ROTATION OF WHEEL : . C = πd = (22/7) x 1. 4 = 4. 4 km : . THE WHEELS MUST COMPLETE 250 ROTATIONS FOR THE CART TO COVER A DISTANCE OF 1. 1 km.

AREA OF CIRCLE CIRCULAR REGION AREA OF THE CIRCLE =πr²

EXAMPLE 1. FIND THE AREA OF A CIRCLE IF ITS RADIUS IS 2. 1 m AREA OF THE CIRCLE =πr² = (22/7) x (2. 1)² = (22/7) x 2. 1 = 22 x 0. 3 x 2. 1 = 22 x 0. 63 = 13. 86 sq m

EXAMPLE 2. THE AREA OF A CIRCULAR PLAYGROUND IS 3850 sq m. WHAT IS RAIDUS ? ANS: AREA OF PLAYGROUND = πr² 3850 = πr² = 3850 r = 35 m