Question
Download Solution PDFr त्रिज्या के एक ठोस धात्विक अर्धगोले को पिघलाया जाता है और आधार त्रिज्या r के एक ठोस लंब वृतीय शंकु में ढाला जाता है। उनके वक्र पृष्ठीय क्षेत्रफलों का अनुपात क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFजैसा कि हम जानते हैं,
अर्धगोला का आयतन = (2/3)πr3
शंकु का आयतन = (1/3)πr2h
प्रश्नानुसार,
(1/3)πr2h = (2/3)πr3
h = 2r
जैसा कि हम जानते हैं,
l2 = r2 + h2
⇒ l2 = r2 + (2r)2
⇒ l2 = 5r2
⇒ l = √5 r
अर्धगोला का वक्र पृष्ठीय क्षेत्रफल = 2πr2
शंकु का वक्र पृष्ठीय क्षेत्रफल = πrl = πr × (√5r) = √5r2
अपेक्षित अनुपात = 2πr2/√5πr2 = 2/√5Last updated on Jul 11, 2025
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