RRB Group D practice question
A solid sphere is melted and recast into 18 identical cones, each having a base radius of 3 cm and height of 18 cm. Find the radius of the sphere.
From a RRB Group D General Awareness practice set · General Awareness
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Correct answer: (A) 9 cm
Volume of one cone = (1/3)πr²h = (1/3)π(3²)(18) = 54π; total volume of 18 cones = 972π. Equating to sphere volume (4/3)πR³ = 972π gives R³ = 729, so R = 9 cm.
हिंदी में प्रश्न
एक ठोस गोले को पिघलाकर 18 समान शंकुओं में ढाला जाता है, जिनमें से प्रत्येक की आधार त्रिज्या 3 सेमी और ऊंचाई 18 सेमी है। गोले की त्रिज्या ज्ञात करें।
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सही उत्तर: (A) 9 सेमी
एक शंकु का आयतन = (1/3)πr²h = (1/3)π(3²)(18) = 54π; 18 शंकुओं का कुल आयतन = 972π। गोले के आयतन (4/3)πR³ = 972π के बराबर रखने पर R³ = 729 मिलता है, अतः R = 9 सेमी।
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