Mensuration Questions for SSC CGL

2D Shapes: Area Formulas

2D shapes form the backbone of Tier-1 questions. You will see direct formula application (find area given side) and reverse problems (find side given area). Rectangle and triangle are most common; trapezoid and rhombus appear occasionally. Circle questions often combine with other shapes (e.g., square inscribed in circle). The key is recognizing which formula applies and plugging numbers correctly — no conceptual depth needed.

• Rectangle: length × width. Diagonal = sqrt(l² + w²)
• Triangle: (1/2) × base × height. Also use Heron's formula for three sides
• Circle: Area = πr², Circumference = 2πr, Arc length = (θ/360) × 2πr
• Trapezoid: (1/2) × (sum of parallel sides) × height
• Rhombus: (1/2) × d1 × d2 (diagonals), or side × height
• Sector of circle: (θ/360) × πr²

3D Solids: Volume & Surface Area

3D questions test volume and surface area of cube, cuboid, cylinder, cone, and sphere. Tier-1 usually asks one formula directly; Tier-2 combines multiple solids or asks for height/radius given volume. Watch for unit conversion (cm to m, liters to cm³). A common trap: confusing lateral surface area (curved part only) with total surface area (including bases).

• Cube: Volume = a³, Total Surface Area = 6a², Lateral SA = 4a²
• Cuboid: Volume = l × w × h, Total SA = 2(lw + wh + lh)
• Cylinder: Volume = πr²h, Total SA = 2πr(r + h), Lateral SA = 2πrh
• Cone: Volume = (1/3)πr²h, Total SA = πr(r + l) where l = slant height, Lateral SA = πrl
• Sphere: Volume = (4/3)πr³, Surface Area = 4πr²
• Hemisphere: Volume = (2/3)πr³, Total SA = 3πr²

Combined & Word Problem Patterns

Tier-2 and harder Tier-1 questions combine shapes or hide the formula in a story. Example: water poured from cylinder into cone, find height. Or: a square field with a circular pond inside, find remaining area. The strategy is to identify each shape, list what you know and what you need, then chain formulas. Watch for implicit constraints (e.g., 'square inscribed in circle' means diagonal of square = diameter of circle).

• Square inscribed in circle: diagonal of square = diameter of circle, so a√2 = 2r
• Circle inscribed in square: diameter of circle = side of square, so 2r = a
• Water transfer problems: equate volumes (e.g., cylinder volume = cone volume)
• Remaining area: total area minus removed area (e.g., circle in square)
• Height/radius reversal: given volume, solve for unknown dimension using algebra

Pi and Unit Conversion Tricks

SSC questions often use π = 22/7 to avoid decimals in answers. However, if answer options have decimals, use π = 3.14. Always check the final unit: if radius is in cm and answer is in m², convert. A litre = 1000 cm³. These conversions are frequent sources of error in Tier-2.

• Use π = 22/7 unless options suggest otherwise
• 1 m = 100 cm, so 1 m² = 10,000 cm²
• 1 litre = 1000 cm³ = 0.001 m³
• Always state units in final answer; marks deducted if missing
• Double-check: if radius is in cm, volume is in cm³, not m³

• Forgetting the 1/3 in cone volume formula — write it as (1/3)πr²h every time, not πr²h/3
• Confusing lateral surface area with total surface area — lateral excludes bases for cylinder and cone
• Using diameter instead of radius in formulas — always convert diameter to radius first (r = d/2)
• Mixing units — if radius is in cm, answer is in cm³ or cm², not m³ or m²; convert at the end if needed
• Forgetting slant height in cone problems — l = sqrt(r² + h²), not just h
• Applying wrong π value — check answer options; if they're whole numbers, likely π = 22/7

• CUBE RULE: 6 faces (6a²), 4 sides (4a²), volume a³ — think 6, 4, 1 powers
• CYLINDER = CIRCLE × HEIGHT: πr² for base, multiply by h, then add 2 bases for SA
• CONE = 1/3 CYLINDER: same base and height, but only 1/3 the volume
• SPHERE = 4/3 CONE: volume is (4/3)πr³, SA is 4πr² (four times the base circle)
• SLANT HEIGHT LADDER: for cone, l² = r² + h² (Pythagoras in disguise)

• Tier-1: Expect 2-3 direct formula questions (area of rectangle, volume of cylinder). Solvable in 60 seconds if formula is memorized. Use π = 22/7 unless told otherwise.
• Tier-2: Combines shapes or hides formula in word problem. Example: 'Water from a cylindrical tank fills a conical vessel. If cylinder radius = 10 cm, height = 20 cm, and cone radius = 5 cm, find cone height.' Requires setting volumes equal and solving for h.
• Recent pattern: Questions on 'remaining area' (e.g., circle cut from square) and 'inscribed/circumscribed' shapes appear frequently. Know the diagonal-diameter relationships cold.
• Calculation speed matters: pre-compute common values (π × 7² = 154, π × 10² = 314 using π = 22/7) to save time.
• Watch for unit tricks: question gives radius in cm, asks answer in m² — convert at the end to avoid errors. Marks are lost on unit mistakes even if calculation is correct.