Question
Download Solution PDFएक लम्ब वृत्तीय बेलन और एक गोले का वक्र पृष्ठीय क्षेत्रफल बराबर है। यदि गोले और बेलन की त्रिज्याएँ क्रमशः 2 और 3 हैं, तो बेलन का कुल पृष्ठीय क्षेत्रफल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
गोले की त्रिज्या, r = 2
बेलन की त्रिज्या, R = 3
लम्ब वृत्तीय बेलन का वक्र पृष्ठीय क्षेत्रफल = गोले का वक्र पृष्ठीय क्षेत्रफल
प्रयुक्त सूत्र:
बेलन का वक्र पृष्ठीय क्षेत्रफल = 2πRh
गोले का वक्र पृष्ठीय क्षेत्रफल = 4πr2
जहाँ r = गोले की त्रिज्या, R = बेलन की त्रिज्या
और, h = बेलन की ऊँचाई
गणना:
प्रश्नानुसार,
⇒ 2πRh = 4πr2
⇒ 2π × (3) × h = 4π × (2)2
⇒ h = 8/3
बेलन का कुल पृष्ठीय क्षेत्रफल = 2πR(R + h)
⇒ 2π(3)(3 + 8/3) = 34π इकाई
∴ सही उत्तर 34π इकाई है।
Last updated on Jul 16, 2025
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