📘 Free Mensuration PDF with Shortcut Tricks, Questions, PYQs, MCQs with Detailed Solutions – Free Download Updated Latest 2025
Mensuration PDF : Are you preparing for competitive exams like SSC, IBPS, SBI, RRB, CDS, CAT, UPSC, or Defence Services? Then you cannot afford to skip Mensuration, one of the most important and high-scoring chapters in Quantitative Aptitude.
To boost your preparation, GovernmentAdda.com offers a completely free Mensuration PDF containing:
✅ Proven Shortcut Tricks
✅ Previous Year Questions (PYQs)
✅ 150+ High-Level MCQs
✅ Diagrams + Formulas
✅ Detailed Step-by-Step Solutions
📥 Download Free Mensuration PDF from GovernmentAdda.com
📚 Table of Contents
- What is Mensuration?
- Importance in Competitive Exams
- Shortcut Tricks for Fast Calculation
- Mensuration Formulas (2D & 3D)
- PYQs with Answers
- 10+ High-Level MCQs with Solutions
- Download Mensuration PDF Free
- FAQs
🧮 What is Mensuration?
Mensuration is the branch of mathematics dealing with the measurement of geometric figures and their parameters such as length, area, volume, and perimeter.
It is broadly categorized into:
- 2D Figures – Square, Rectangle, Circle, Triangle, Parallelogram, Rhombus, Trapezium
- 3D Figures – Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere
📈 Importance of Mensuration in Exams
| Exam | Expected Questions | Difficulty |
|---|---|---|
| SSC CGL/CHSL | 4–6 | Medium–Hard |
| Banking (IBPS/SBI) | 2–4 | Medium |
| CAT | 3–5 | Hard |
| CDS/NDA | 5–7 | Medium–Hard |
| Railways/Defence | 3–6 | Medium |
Mensuration is formula-based and easy to score if you’re well-prepared with tricks and concepts.
⚡ Shortcut Tricks to Crack Mensuration Fast
🔹 Trick #1: For Square and Rectangle
- Area of Square = Side²
- Area of Rectangle = Length × Breadth
- 🔁 If perimeter is constant, Square gives maximum area
🔹 Trick #2: Circle-Related Ratios
- If radius becomes n times, then:
→ Area becomes n² times
→ Circumference becomes n times
🔹 Trick #3: Volume & Surface Area Relation
For similar shapes:
- If ratio of sides is a : b
→ Surface Area ratio = a² : b²
→ Volume ratio = a³ : b³
🔹 Trick #4: Cone & Cylinder Combo
- Height, Radius same ⇒ Volume of cone is 1/3rd of the cylinder
🧾 Important Mensuration Formulas (Quick Reference)
📐 2D Figures
| Shape | Area | Perimeter |
|---|---|---|
| Square | a² | 4a |
| Rectangle | l × b | 2(l + b) |
| Circle | πr² | 2πr |
| Triangle | ½ × b × h | a + b + c |
| Rhombus | ½ × d₁ × d₂ | 4a |
| Trapezium | ½ × (a + b) × h | a + b + c + d |
📦 3D Figures
| Shape | Volume | Surface Area |
|---|---|---|
| Cube | a³ | 6a² |
| Cuboid | l × b × h | 2(lb + bh + hl) |
| Cylinder | πr²h | 2πr(h + r) |
| Cone | ⅓πr²h | πr(l + r) |
| Sphere | 4/3πr³ | 4πr² |
| Hemisphere | 2/3πr³ | 3πr² |
🧪 PYQs (Previous Year Questions) with Answers
PYQ 1: SSC CGL 2022
Q: What is the volume of a cylinder with radius 7 cm and height 10 cm?
Sol: Volume = πr²h = 22/7 × 7 × 7 × 10 = 1540 cm³
PYQ 2: IBPS PO 2021
Q: A cone has a height of 12 cm and radius 5 cm. Find its volume.
Sol: Volume = (1/3)πr²h = (1/3)×(22/7)×25×12 = 314.29 cm³
PYQ 3: RRB JE 2019
Q: Find the surface area of a cube whose side is 4 cm.
Sol: SA = 6a² = 6×16 = 96 cm²
🧠 10 High-Level MCQs with Detailed Solutions
Q1. A square has a side of 14 cm. Find the area and perimeter.
A: Area = 14² = 196 cm²; Perimeter = 4×14 = 56 cm
Q2. The radius and height of a cone are 3 cm and 4 cm. Find the slant height.
Sol: l = √(r² + h²) = √(9 + 16) = 5 cm
Q3. A circular park has a radius of 21 m. Find its area.
Sol: Area = πr² = 22/7 × 441 = 1386 m²
Q4. Volume of a cuboid is 120 cm³. Its length is 5 cm and breadth is 4 cm. Find the height.
Sol: h = V / (l × b) = 120 / 20 = 6 cm
Q5. If the side of a cube is doubled, its volume becomes:
Sol: Volume ∝ a³ ⇒ New volume = (2a)³ = 8a³ ⇒ 8 times
Q6. Find the total surface area of a cylinder with radius 3 cm and height 7 cm.
Sol: TSA = 2πr(h + r) = 2×22/7×3×(7+3) = 188.57 cm²
Q7. A cone and cylinder have equal radii and heights. What is the ratio of their volumes?
Sol: Ratio = 1:3 (Cone: Cylinder)
Q8. A hemisphere has a radius of 5 cm. Find its total surface area.
Sol: TSA = 3πr² = 3×22/7×25 = 235.71 cm²
Q9. Area of a trapezium with bases 10 cm and 14 cm and height 6 cm?
Sol: A = ½(a+b)×h = ½(24)×6 = 72 cm²
Q10. A rectangle has length 10 m and breadth 8 m. What is the diagonal?
Sol: Diagonal = √(l² + b²) = √(100 + 64) = √164 ≈ 12.8 m
📥 Download Mensuration PDF for Free by GovernmentAdda.com
What’s Inside the PDF:
- 📘 100+ MCQs (All difficulty levels)
- ✏️ SSC, Bank, CAT, UPSC-specific sets
- 📊 Diagrams & Stepwise Solutions
- ✅ Formula Sheets
- 📌 CGL Tier-I & Tier-II Practice Sets
📥 Click Here to Download Mensuration PDF – GovernmentAdda.com
🙋 Frequently Asked Questions (FAQs)
Q1. Is the Mensuration PDF really free?
✅ Yes, absolutely free and accessible at GovernmentAdda.com.
Q2. Is this PDF helpful for SSC CGL Tier 1 and 2?
✅ Yes, it includes separate sets for both levels.
Q3. Are formulas and diagrams included?
✅ Yes, visual explanations and formula sheets are part of the PDF.
Q4. Can I prepare for CAT and CDS exams with this?
✅ Yes, advanced questions are included for MBA and defence aspirants.
Q5. Are previous year questions included?
✅ Yes, over 50 PYQs from SSC, Bank, and CAT are included.
🏁 Final Words
Mensuration is not just about remembering formulas — it’s about applying them with logic and speed. With the Free Mensuration PDF by GovernmentAdda.com, you get:
✅ Formula Cheat Sheets
✅ PYQs & Mock Sets
✅ 150+ Practice Questions
✅ Visual & Conceptual Clarity
👉 Download the PDF Now & Boost Your Score!
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Complete Question Bank with Answers PDF
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