लंब गोलाकार शंकुचे घनफळ, ज्याच्या पायाची त्रिज्या त्याच्या उंचीच्या 5/9 व्या भाग आणि गोळ्याच्या घनफळाच्या समान आहे. गोलाच्या शंकूच्या त्रिज्येचे गुणोत्तर काय आहे?

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RRC Group D Previous Paper 28 (Held On: 26 Sept 2018 Shift 2)
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लंब वृत्‍तीय शंकु:

उंची = h आणि त्रिज्या = r

दिलेले, तर पायाची त्रिज्या त्याच्या उंचीच्या पाच-नवव्या भागाइतकीच आहे:

∴ r = 5h/9

⇒ h = 9r/5

लंब वृत्‍तीय शंकुचे घनफळ =  π/3 × r2 × h

= π/3 × r2 × 9r/5

= 3π/5 × r3

आणि

R त्रिज्या असलेल्या गोलाचे घनफळ = 4π/3 × R3

दोन आकृत्यांचे घनफळ समान असल्यामुळे:

3π/5 × r= 4π/3 × R3

⇒ r3/R= 20/9

⇒ r3/R= 60/27

⇒ r : R = 

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