लोहे की एक बेलनाकार छड़ जिसकी ऊंचाई इसकी त्रिज्या से बारह गुना है, को पिघलाकर गोलाकार गेंदों में ढाला जाता है, जिनमें से प्रत्येक की त्रिज्या, बेलन की त्रिज्या की एक तिहाई है। गोलाकार गेंदों की संख्या ज्ञात कीजिए। 
Subject: Quantitative Aptitude | Topic: Mensuration (2D & 3D) | Difficulty: MEDIUM
Options
- (A) 243
- (B) 198
- (C) 224
- (D) 212
Verified Answer
Option (A): 243
10-Second Shortcut Trick
⚡ 10-Second Exam Shortcut: Eliminate options ending in incorrect units or calculate unit digits first before solving full arithmetic.
Step-by-Step Derivation
- Cylinder radius R, height H = 12R, so volume = πR²H = 12πR³; each small sphere has radius R/3, volume = (4/3)π(R/3)³ = 4πR³/81.
- Number of spheres = 12πR³ ÷ (4πR³/81) = 12 × 81/4 = 243.
- The official Ans column ticks option 1, matching this check.
Common Trap to Avoid
⚠️ Common Trap: Misreading inverse proportions or rushing calculation in the last algebraic step.
Exam Tip
💡 Exam Tip: Always verify if question asks for perimeter, area, or remaining fraction.
Related Practice Questions in Mensuration (2D & 3D)
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Practice more Mensuration (2D & 3D) questions in SSC CGL Complete Test Series 2026.
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