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पृष्ठीय क्षेत्रफल और आयतन

Question
CBSEHHIMAH10010496
Wired Faculty App

एक लचीली बैल्ट को एक घिरनी (pulley), जिसकी त्रिज्या 5 सेमी है, के गिर्द लपेटा गया है। (आकृति 10) बैल्ट के एक बिंदु C से लचीली बैल्ट को केंद्र O से सीधा इस प्रकार खींचा जाता है की वह बिंदु P पर पहुँच जाता है जहॉं OP = 10 सेमी है। बैल्ट के उस भाग की लम्बाई ज्ञात कीजिए जो अब भी घिरनी के साथ लगा है। रेखांकित भाग का क्षेत्रफल भी ज्ञात कीजिए। left parenthesis straight pi space equals space 3.14 space तथ ा space square root of 3 space equals space 1.73 space ल ी ज ि ए right parenthesis
                            

Solution
angle OAP space equals space 90 degree space space आयत space म ें space increment OAP comma space space space space space space space cos space straight theta space equals space begin inline style OA over OA end style space equals space begin inline style 5 over 10 end style space equals space begin inline style 1 half end style space equals space cos space 60 degree space space space space space space space space therefore space straight theta space equals space 60 degree angle AOB space equals space 60 degree space plus space 60 degree space equals space 120 degree space space space space space space space space space space space space space space....... left parenthesis straight i right parenthesis space प ् रत ि ब िं ब space angle AOB space equals space 360 degree space minus space angle AOB space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 360 degree space minus space 120 degree space equals space 240 degree space space space space space space space space space space space space space space space space space space space space space space space space straight alpha space equals space 240 degree space ब ै ल ् ट space क ा space ल ें स space ज ो space अभ ी space भ ी space प ु ल ि space क े space स ा थ space स ं पर ् क space म ें space ह ै space equals space ABD space equals space प ् रम ु ख space व ृ त ् त minus च ा प space क े space ल ें स space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis begin inline style fraction numerator straight alpha over denominator 360 degree end fraction end style right parenthesis 2 πr space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space begin inline style fraction numerator 240 degree over denominator 360 degree end fraction end style space straight x space 2 space straight x space 3.14 space straight x space 5 space equals space 20.93 space cm आयत space म ें space increment OAP comma space space space space space space space space space space sin space 60 degree space equals space begin inline style AP over OP end style rightwards double arrow space begin inline style fraction numerator square root of 3 over denominator 2 end fraction end style space equals space begin inline style AP over 10 end style rightwards double arrow space AP space equals space 5 square root of 3 space cm क ् ष े त ् रफल space increment OAP space equals space begin inline style 1 half end style space straight x space आध ा र space straight x space space ऊ ँ च ा ई space space space space space space space space space space space space space space space space space space space space space space space space space space equals space begin inline style 1 half end style space straight x space AP space straight x space OA space space space space space space space space space space space space space space space space space space space space space space space space space space equals space begin inline style 1 half end style straight x space 5 square root of 3 space straight x space 5 space equals begin inline style 25 over 2 end style square root of 3 space cm squared
left parenthesis increment OAP right parenthesis space equals space left parenthesis increment OBP right parenthesis space begin inline style 25 over 2 end style square root of 3 space cm squared म ा म ू ल ी space क ् ष े त ् र space क ा space क ् ष े त ् रफल space OACB space equals space begin inline style fraction numerator straight theta over denominator 360 degree end fraction end style πr squared equals space begin inline style fraction numerator 120 degree over denominator 360 degree end fraction end style space straight x space 3.14 space straight x space left parenthesis 5 right parenthesis squared space space space space space space space space space space space space space space.......... space left parenthesis straight i right parenthesis space स े comma equals space begin inline style fraction numerator 78.5 over denominator 3 end fraction end style space equals 26.16 space equals 36.14 space cm squared छ ा य ां क ि त space क ् ष े त ् रफल space equals space left parenthesis increment OAP right parenthesis space equals space left parenthesis increment OBP right parenthesis space minus space म ा म ू ल ी space क ् ष े त ् र space क ा space क ् ष े त ् रफल space OACB equals space begin inline style fraction numerator 25 square root of 3 over denominator 2 end fraction end style space plus space begin inline style fraction numerator 25 square root of 3 over denominator 2 end fraction end style space minus space 26.17 equals space 25 square root of 3 space minus space 26.17 equals space 25 left parenthesis 1.73 right parenthesis space minus space 26.17 equals space 43.25 space minus space 26.17 space equals space 17.08 space cm squared

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