Question
Download Solution PDF4 सेमी त्रिज्येची तीन वर्तुळे एकमेकांना स्पर्श करत आहेत. या तीन वर्तुळांभोवती दोरी घट्ट बांधलेली आहे. दोरीची लांबी किती आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्याप्रमाणे:
4 सेमी त्रिज्येची तीन वर्तुळे एकमेकांना स्पर्श करत आहेत.
गणना:
वर्तुळाच्या संपर्कात नसलेल्या दोरीची लांबी = 2r + 2r + 2r
⇒ 6r = 6 × 4
⇒ 24
जसे आपण म्हणू शकतो की दोरीने व्यापलेला कोन 120º आहे
किंवा आपण असे म्हणू शकतो की दोरीने वर्तुळाचा 1/3 भाग व्यापला आहे
स्ट्रिंग टचिंग वर्तुळाची लांबी = 2πr/3 2πr/3 2πr/3
⇒ 2πr = 2 × 4 × π
⇒ 8π
एकूण लांबी = 24 8π
∴ आवश्यक उत्तर 24 + 8p सेमी आहे. (येथे pi म्हणजे π)
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