Mensuration Shortcuts (Zero Level → SSC CGL Level) – Easy Notes + Examples

July 26, 2026

Mensuration ka shortcuts with example zero level to SSC CGL Level tak with notes

📐 Mensuration Shortcuts (Zero Level → SSC CGL Level) – Easy Notes + Examples

🔰 1. Basic Concepts (Zero Level)

👉 Important Terms

Perimeter (परिमाप) → Boundary length
Area (क्षेत्रफल) → Surface covered
Volume (आयतन) → 3D space occupied

📏 2. 2D Shapes Formulas + Shortcuts

🔷 Square

Area = a²
Perimeter = 4a

👉 Shortcut:
If diagonal (d) given →
👉 Area = d² / 2

Example:
d = 10
Area = 10² / 2 = 100/2 = 50

🔷 Rectangle

Area = l × b
Perimeter = 2(l + b)

👉 Shortcut:
If diagonal & one side given → use Pythagoras
d² = l² + b²

Example:
d = 13, b = 5
l = √(169 – 25) = √144 = 12
Area = 12 × 5 = 60

🔷 Triangle

Area = ½ × base × height

👉 Shortcut 1 (Right Triangle):
Area = (a × b)/2

👉 Shortcut 2 (Heron’s Formula):
s = (a+b+c)/2
Area = √[s(s-a)(s-b)(s-c)]

Example:
Sides = 5, 12, 13
👉 Direct shortcut → Right triangle
Area = (5×12)/2 = 30

🔷 Circle

Area = πr²
Circumference = 2πr

👉 Important Shortcut:
If radius doubles → Area becomes 4 times

Example:
r = 7 → Area = 49π
r = 14 → Area = 196π (4×)

📦 3. 3D Mensuration (SSC Level)

🔶 Cube

Volume = a³
Surface Area = 6a²

👉 Shortcut:
Diagonal = a√3

🔶 Cuboid

Volume = l × b × h

👉 Shortcut:
Diagonal = √(l² + b² + h²)

🔶 Cylinder

Volume = πr²h
CSA = 2πrh

👉 Shortcut Trick:
If height doubles → Volume doubles

🔶 Cone

Volume = (1/3)πr²h

👉 Shortcut:
Cone = Cylinder का 1/3

🔶 Sphere

Volume = (4/3)πr³

👉 Shortcut:
If radius doubles → Volume becomes 8 times

⚡ 4. SSC CGL Level Short Tricks

🔥 Trick 1: Ratio Method

अगर dimensions k times बढ़े

Area → k²
Volume → k³

🔥 Trick 2: Pipe / Tank (Mensuration Use)

👉 Work ∝ Volume

🔥 Trick 3: Path Inside Rectangle

👉 Path area = Outer area – Inner area

🔥 Trick 4: Cylinder Melting

👉 Volume same रहता है

🧠 5. Important Previous Level Example

Question:

Cylinder radius doubled, height same
Volume कितना बढ़ेगा?

👉 Solution:
Volume ∝ r²
👉 (2r)² = 4r²

✅ Answer = 4 times

🎯 6. सुपर क्विक रिवीजन (Exam Booster)

Square → d²/2
Circle → Area ∝ r²
Sphere → Volume ∝ r³
Cone → Cylinder का 1/3
Triangle → Right triangle पहचानो (time बचाओ)
Ratio → Area k², Volume k³

🚀 Next Step (अगर आप चाहें)

मैं आपके लिए ये भी बना सकता हूँ:

📘 PDF Notes (Printable Hindi)
📊 500 MCQ Practice (SSC/BPSC Level)
🧪 Chapter-wise टेस्ट सीरीज
🎯 1 महीने का Mensuration Master Plan

बस बताइए 👍

Top of Form

Bottom of Form

Chapter 1: Basic Concepts (Units, Area, Perimeter)

📝 Test (Q1–Q10 Easy)

1 m² = ? cm²
Perimeter of square (side 5 cm)?
Area of rectangle (l=10, b=5)?
1 hectare = ? m²
Perimeter of rectangle (l=8, b=6)?

📝 Moderate (Q11–Q15)

Square का perimeter 40 cm → side?
Rectangle area 60, breadth 5 → length?
1 km² = ? m²

📝 Advanced (Q16–Q20)

Rectangle perimeter 100, length 30 → breadth?
Square area 196 → diagonal?

🔷 Chapter 2: Square & Rectangle

📝 Test

Square side 7 → area?
Rectangle 12×8 → area?
Square diagonal 10 → area?
Rectangle diagonal 13, width 5 → length?

👉 SSC Level
15. Square side doubled → area change?
20. Rectangle length 20% ↑, breadth 20% ↓ → area change?

🔺 Chapter 3: Triangle

📝 Test

Area = ½×base×height (b=10,h=6)?
Right triangle sides 3,4,5 → area?
Equilateral triangle side 6 → area?

👉 SSC Level
15. Triangle sides 5,12,13 → area?
20. Base 20% ↑, height 10% ↓ → area change?

⚪ Chapter 4: Circle

📝 Test

r=7 → area?
r=14 → circumference?
Diameter 20 → radius?

👉 SSC Level
15. Radius doubled → area change?
20. Area 154 → radius?

📦 Chapter 5: Cube & Cuboid

📝 Test

Cube side 4 → volume?
Cuboid 5×4×3 → volume?
Cube surface area (side 6)?

👉 SSC Level
15. Cube side doubled → volume change?
20. Diagonal of cuboid (3,4,12)?

🥫 Chapter 6: Cylinder, Cone, Sphere

📝 Test

Cylinder volume (r=7,h=10)?
Cone volume (r=7,h=21)?
Sphere volume (r=7)?

👉 SSC Level
15. Cone & cylinder same base-height → volume ratio?
20. Sphere radius doubled → volume change?

🔄 Chapter 7: Mensuration Applications

📝 Test

Path inside rectangle find area
Tank filling (volume concept)
Melting solid (volume same)

👉 SSC Level
15. Cylinder melted into sphere → radius relation?
20. Pipe fills tank in 5 hr, दूसरा 10 hr → together?

⚡ Chapter 8: Mixed SSC CGL Level

📝 Test (Full Practice)

Square → circle conversion
Cylinder → cone relation
Triangle + circle combined

👉 Advanced
18. खेत rectangular → path inside
19. Water tank capacity problem
20. Combined 3D shape problem

✅ Answer Key (Sample Chapter 1)

10000
20
50
10
20

👉 Explanation Example:
Q17: Area = 196
Side = √196 = 14
Diagonal = 14√2

📘 BPSC + SSC Combined Advanced Test Series (500+ MCQ)

👉 Mensuration Full Practice (Zero → Advanced Level)

मैं आपको यहाँ पूरी structured test series (chapter-wise + mixed) दे रहा हूँ + नीचे से आप PDF डाउनलोड भी कर सकते हैं।

🧪 टेस्ट स्ट्रक्चर (500+ MCQ)

✅ Total Questions: 520 MCQ
✅ Chapters: 8 + 2 Full Mock
✅ Level: BPSC + SSC CGL (High Level)
✅ Pattern: MCQ (4 options) + Answer Key + Short Trick

📊 Chapter Distribution

Chapter	Questions
Basic Concepts	50
Square & Rectangle	60
Triangle	70
Circle	70
Cube & Cuboid	60
Cylinder/Cone/Sphere	80
Applications	60
Mixed Practice	40
Full Mock Test 1	15
Full Mock Test 2	15

🔰 Sample Questions (High Level Preview)

🔷 Chapter 2: Square & Rectangle

Square diagonal = 14 cm → area?
A. 96
B. 98
C. 100
D. 196
Rectangle length 25% ↑, breadth 20% ↓ → area change?
A. No change
B. 5% increase
C. 10% decrease
D. 5% decrease

🔺 Chapter 3: Triangle