🎙 Teacher-Style Introduction

Mensuration 3D में हम वस्तुओं के कुल पृष्ठीय क्षेत्रफल (Total Surface Area – TSA), वक्र पृष्ठीय क्षेत्रफल (Curved Surface Area – CSA) और आयतन (Volume) सीखते हैं। Delhi Police Exam में 1–2 आसान सवाल आते हैं, mostly cuboid, cylinder और sphere से।

📘 Important Formulas / मुख्य सूत्र

⚡ Tricks & Exam Shortcuts

• Cylinder & cube are most common in DP exams.
• CSA = curved (side) area; TSA = total (includes top & bottom).
• Volume always in cubic units (cm³, m³).
• Always note radius vs diameter — DP exam में trick यही है।
• Slope length (l) in cone → l = √(r² + h²).

✔ Solved Examples / हल प्रश्न

Example 1: Cuboid: l=6, b=4, h=3 TSA = 2(lb + lh + bh) = 2(24 + 18 + 12) = 108

Example 2: Cube: side=5 TSA = 6a² = 150 Volume = 125

Example 3: Cylinder: r=7, h=10 CSA = 2πrh = 2×22/7×7×10 = 440 Volume = πr²h = 22/7×49×10 = 1540

Example 4: Cone: r=7, h=24 l = √(7²+24²)=25 CSA = πrl = 22/7×7×25 = 550

Example 5: Sphere: r=7 TSA = 4πr² = 4×22/7×49 = 616

Example 6: Hemisphere r=3 TSA = 3πr² = 3×3×3×22/7 = 84.85 approx

Example 7: Cylinder diameter=14 (radius=7), height=5 TSA = 2πr(r+h)=2×22/7×7×12 = 528

Example 8: Cube edge=4 → diagonal = a√3 = 4√3

✔ MCQs (Delhi Police Pattern)

1. Cuboid l=4,b=3,h=2 → volume = 24
2. Cube side=6 → TSA = 216
3. Cylinder r=7,h=7 → CSA = 308
4. Sphere r=14 → TSA = 2464
5. Cone r=5,h=12 → l=13 → CSA = 65π
6. Cylinder diameter=10,h=14 → r=5 → volume = 1100π
7. Hemisphere r=7 → CSA = 308
8. Cube side=3 → diagonal = 3√3
9. Cuboid TSA if l=2,b=3,h=4 → 52
10. Cone volume formula? → ⅓ πr²h

💡 Motivation: बड़े chapter को आसान बनाना ही practice की असली ताकत है — यही Shyamsthali spirit! 🚓🔥