SSC GD Mensuration Questions: Download Free PDF & Practice Now

Preparing for the SSC GD Constable exam? You are probably working hard on your running and physical fitness. But remember, the written exam is the first hurdle you need to cross. In the Math section, there is one topic that scares almost every student aspirant, which is Mensuration. When you see questions about “Cylinders,” “Cones,” or “Area of a Field,” do you feel like skipping them? Don’t do that! Here is the secret: Mensuration in SSC GD is not hard; it is just formula-based. You don’t need deep logic like in Profit & Loss. If you simply remember the formula for the Volume of a Cylinder or the Area of a Circle, you can solve these. It’s that direct. To help you score these easy marks, we have collected the most important Mensuration questions from previous years. We have compiled them into a Free PDF that you can download below.

Why is Mensuration Important for SSC GD?

In the SSC GD exam, you will find 2 to 3 questions from Mensuration. That might not sound like a lot, but in a competitive exam, 4-6 marks can decide if you get your dream post or not.

• Direct Formulas: The questions are usually straightforward. Example: “The radius is 7, find the Area.”
• No Tricks: Unlike other topics, examiners rarely twist the language here.
• Rank Booster: Most students skip this because they hate memorizing formulas. If you attempt it, you automatically go ahead of them.

Important Topics: What to Study?

Mensuration is divided into two parts. You need to focus on specific shapes for SSC GD.

1. 2D Mensuration (Area & Perimeter):
   • Square & Rectangle: Basic area and perimeter.
   • Circle: Circumference and area. Questions on “Wheel rotation” are very common.
   • Triangle: Equilateral and Right-angled triangles.
2. 3D Mensuration (Volume & Surface Area):
   • Cube & Cuboid: Volume and total surface area.
   • Cylinder & Cone: Very important. Memorize the volume formulas (pir²h, etc.).
   • Sphere & Hemisphere: Simple radius-based questions.

Download Free PDF of Mensuration Questions for SSC GD

We have prepared a comprehensive PDF containing exam-level Mensuration questions. We have chosen questions that are not too hard and not too easy, just the perfect SSC GD level. You can download it for free and keep it on your phone for quick revision.

Q1. The length and breadth of a rectangle are in the ratio 4:3. If the area is 300 cm², find the perimeter.
(a) 60 cm
(b) 70 cm
(c) 80 cm
(d) 50 cm
Answer: (b) 70 cm
Logic: 4x × 3x = 300 ⇒ 12x² = 300 ⇒ x² = 25 ⇒ x = 5.
L = 20, B = 15.
Perimeter = 2(20 + 15) = 70.

Q2. Find the volume of a cylinder whose radius is 7 cm and height is 10 cm.
(a) 1540 cm³
(b) 1400 cm³
(c) 1600 cm³
(d) 1350 cm³
Answer: (a) 1540 cm³
Logic: Volume = πr²h = (22/7) × 7 × 7 × 10 = 1540.

Q3. The diagonal of a square is 10√2 cm. Find its area.
(a) 50 cm²
(b) 100 cm²
(c) 200 cm²
(d) 150 cm²
Answer: (b) 100 cm²
Logic: Diagonal = a√2 ⇒ a = 10.
Area = a² = 100.

Q4. If the radius of a sphere is doubled, its volume becomes:
(a) 2 times
(b) 4 times
(c) 8 times
(d) 6 times
Answer: (c) 8 times
Logic: Volume ∝ r³.
If r becomes 2r, volume becomes 2³ = 8 times.

Q5. The circumference of a circle is 88 cm. Find its area.
(a) 616 cm²
(b) 515 cm²
(c) 400 cm²
(d) 350 cm²
Answer: (a) 616 cm²
Logic: 2πr = 88 ⇒ r = 14.
Area = πr² = (22/7) × 14 × 14 = 616.

Q6. Find the Total Surface Area of a cube of side 5 cm.
(a) 125 cm²
(b) 100 cm²
(c) 150 cm²
(d) 175 cm²
Answer: (c) 150 cm²
Logic: TSA = 6a² = 6 × 25 = 150.

Q7. A wheel makes 1000 revolutions to cover a distance of 88 km. The radius of the wheel is:
(a) 7 m
(b) 14 m
(c) 21 m
(d) 28 m
Answer: (b) 14 m
Logic: Distance = 1000 × 2πr = 88000 m.
Solve for r ⇒ r = 14 m.

Q8. The curved surface area of a cone with radius 7 cm and slant height 10 cm is:
(a) 220 cm²
(b) 210 cm²
(c) 230 cm²
(d) 200 cm²
Answer: (a) 220 cm²
Logic: CSA = πrl = (22/7) × 7 × 10 = 220.

Q9. The length of the longest pole that can be placed in a room of dimensions 10 × 10 × 5 m is:
(a) 10 m
(b) 15 m
(c) 20 m
(d) 12 m
Answer: (b) 15 m
Logic: Diagonal = √(10² + 10² + 5²) = √225 = 15 m.

Q10. Two cylinders have equal height and their radii are in ratio 1:2. The ratio of their volumes is:
(a) 1:2
(b) 1:4
(c) 2:1
(d) 4:1
Answer: (b) 1:4
Logic: Volume ∝ r² (height same).
Ratio = 1² : 2² = 1 : 4.

MENSURATION FORMULA SHEET (SSC GD)

1. Basic Terms

• Perimeter: Total boundary length of a closed figure.
• Area: Space covered inside a 2D shape.
• Volume: Space occupied inside a 3D object.
• CSA: Curved Surface Area
• TSA: Total Surface Area

2D SHAPES

2. Square

• Side = a
• Perimeter = 4a
• Area = a²
• Diagonal = a√2

3. Rectangle

• Length = l, Breadth = b
• Perimeter = 2(l + b)
• Area = l × b
• Diagonal = √(l² + b²)

4. Triangle

• Area = (1/2) × base × height
• Perimeter = a + b + c
• Heron’s Formula:
  s = (a + b + c)/2
  Area = √[s(s – a)(s – b)(s – c)]

5. Right Triangle

• Pythagoras: Hypotenuse² = Base² + Height²
• Area = (1/2) × base × height

6. Parallelogram

• Area = base × height
• Perimeter = 2(a + b)

7. Rhombus

• All sides equal
• Area = (1/2) × (d1 × d2)
• Perimeter = 4a

8. Trapezium

• Area = (1/2) × (sum of parallel sides) × height
  = (1/2) × (a + b) × h

9. Circle

• Radius = r, Diameter = 2r
• Circumference = 2πr
• Area = πr²
• π = 22/7 or 3.14

3D SHAPES

10. Cube

• Side = a
• TSA = 6a²
• LSA (CSA) = 4a²
• Volume = a³
• Diagonal = a√3

11. Cuboid

• Length = l, Breadth = b, Height = h
• TSA = 2(lb + bh + hl)
• LSA = 2h(l + b)
• Volume = l × b × h
• Diagonal = √(l² + b² + h²)

12. Cylinder

• Radius = r, Height = h
• CSA = 2πrh
• TSA = 2πr(r + h)
• Volume = πr²h

13. Cone

• Radius = r, Height = h, Slant height l
• l = √(r² + h²)
• CSA = πrl
• TSA = πr(r + l)
• Volume = (1/3)πr²h

14. Sphere

• Radius = r
• TSA = 4πr²
• Volume = (4/3)πr³

15. Hemisphere

• Radius = r
• TSA = 3πr²
• CSA = 2πr²
• Volume = (2/3)πr³

SPECIAL FORMULAS (SSC GD MUST-KNOW)

16. Perimeter of Semicircle

• Perimeter = πr + 2r
• Area = (1/2)πr²

17. Annulus (Ring)

• Outer radius = R, Inner radius = r
• Area = π(R² – r²)

18. Conversion Values

• 1 m = 100 cm
• 1 cm = 10 mm
• 1 m² = 10,000 cm²
• 1 hectare = 10,000 m²
• 1 km² = 10,00,000 m²

19. Shortcut Values

• Square of 1–30 (memorize for area questions)
• Use π = 22/7 for exact, π = 3.14 for approx.

20. Most Important SSC GD Tip
    Always identify if the question is about:

• Perimeter,
• Area,
• CSA,
• TSA, or
• Volume

Most mistakes happen because students use the wrong formula.

How to Prepare Mensuration for SSC GD?

Math is not about magic; it’s about method. Here is how you can master Mensuration easily:

• Make a Formula Chart: This is the most important step. Write down all formulas (Cube, Cone, Cylinder, Sphere) on paper and stick it on your wall. Read it every morning.
• Understand the Difference: Don’t get confused between “Volume” and “Surface Area.”
  • Volume = How much water it can hold.
  • Surface Area = How much paper is needed to wrap it?
• Value of Pi: Always remember pi = 22/7. Most answers in the exam will be multiples of 11 (like 154, 88, 616). This is a great trick to guess answers!
• Practice Calculation: Mensuration questions involve multiplication. Improve your calculation speed so you don’t waste time doing 22 x 14 x 15 in the exam.
• Attempt Topic Tests: Once you learn the formulas, test yourself. Attempt Free Topic Tests to see if you can recall the right formula at the right time.

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FAQs: Mensuration Questions for SSC GD

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