Mensuration Questions for RRB NTPC: Download Free PDF & Practice Now

Dreaming of a job in the Indian Railways? The RRB NTPC exam is your gateway. But let’s be honest—while General Awareness is fun to read, the Mathematics section gives many students sleepless nights. And within Math, there is one villain that scares everyone: Mensuration. Seeing formulas like 2πrh or (4/3)πr³ can be confusing. You might feel like skipping this topic. But here is the truth: In RRB NTPC, Mensuration is actually the easiest part of Advanced Math. Why? Because, unlike Geometry, where you need to prove theorems, Mensuration is purely formula-based. If you memorize the formula, you get the answer. It’s that simple. To help you conquer this fear, in this blog, we have provided the most important Mensuration questions for RRB NTPC exam.

Why is Mensuration Important for RRB NTPC?

In both CBT-1 and CBT-2, Advanced Math plays a huge role. You can expect 3 to 4 questions from Mensuration alone.

• Direct Marks: The questions are usually direct applications of formulas. Example: “Find the volume of a sphere with radius 7.”
• No Guesswork: In GK, you might get confused between two options. In Mensuration, if your calculation matches an option, you know you are 100% correct.
• Rank Decider: Most candidates are weak in this area. If you score here, you jump ahead of lakhs of competitors.

Important Topics: What to Study?

You don’t need to study everything. RRB NTPC focuses on specific shapes.

1. 2D Shapes (Area & Perimeter):
   • Circle & Semi-Circle: Very important. Questions on “Wire bent into a circle” are common.
   • Triangles: Equilateral and Isosceles triangles.
   • Quadrilaterals: Rhombus, Trapezium, and Parallelogram.
2. 3D Shapes (Volume & Surface Area):
   • Cylinder & Cone: Memorize the Curved Surface Area (CSA) and Total Surface Area (TSA).
   • Sphere & Hemisphere: Simple volume questions.
   • Cube & Cuboid: Length of the longest rod (diagonal) in a room.

Download Free PDF of Mensuration Questions for RRB NTPC

We have carefully analyzed many previous year question papers, such as questions difficulty level, the pattern of the questions, and much more. After analyzing the papers, we have created some mensuration questions for RRB NTPC that will help you boost your exam preparation. We have compiled it in a PDF that you can download for free by clicking on the button given below.

Q1. The radius of a wheel is 21 cm. How much distance will it travel in 10 revolutions?
(a) 1320 cm
(b) 1400 cm
(c) 1500 cm
(d) 1200 cm
Answer: (a) 1320 cm
Logic: Distance in 1 rev = 2πr = 2 × (22/7) × 21 = 132 cm.
In 10 revs = 132 × 10 = 1320 cm.

Q2. Find the volume of a sphere whose radius is 3 cm.
(a) 36π
(b) 27π
(c) 18π
(d) 40π
Answer: (a) 36π
Logic: Volume = (4/3)πr³ = (4/3) × π × 27 = 36π.

Q3. The length of the longest rod that can be placed in a room 10m × 10m × 5m is:
(a) 15 m
(b) 20 m
(c) 25 m
(d) 12 m
Answer: (a) 15 m
Logic: Diagonal = √(10² + 10² + 5²) = √225 = 15 m.

Q4. The ratio of the radii of two cylinders is 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is:
(a) 20:27
(b) 10:9
(c) 4:9
(d) 27:20
Answer: (a) 20:27
Logic: Volume ratio = r₁²h₁ : r₂²h₂ = (2² × 5) : (3² × 3) = 20 : 27.

Q5. The area of an equilateral triangle is 16√3 cm². Find its side.
(a) 4 cm
(b) 8 cm
(c) 12 cm
(d) 16 cm
Answer: (b) 8 cm
Logic: (√3/4)a² = 16√3 ⇒ a²/4 = 16 ⇒ a² = 64 ⇒ a = 8.

Q6. If the diagonal of a cube is √12 cm, then its volume is:
(a) 8 cm³
(b) 12 cm³
(c) 24 cm³
(d) 6 cm³
Answer: (a) 8 cm³
Logic: Diagonal = a√3 ⇒ a√3 = √12 = 2√3 ⇒ a = 2.
Volume = a³ = 8.

Q7. The perimeter of a rectangle is 40 cm and its length is 12 cm. Find its breadth.
(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 6 cm
Answer: (a) 8 cm
Logic: 2(L + B) = 40 ⇒ L + B = 20.
B = 20 – 12 = 8.

Q8. A wire is in the form of a circle of radius 28 cm. It is bent into a square. Find the side of the square.
(a) 44 cm
(b) 34 cm
(c) 22 cm
(d) 11 cm
Answer: (a) 44 cm
Logic: Perimeter of circle = 2πr = 2 × (22/7) × 28 = 176.
4a = 176 ⇒ a = 44.

Q9. The curved surface area of a cylinder of height 14 cm is 88 cm². The diameter of the cylinder is:
(a) 2 cm
(b) 1 cm
(c) 3 cm
(d) 4 cm
Answer: (a) 2 cm
Logic: 2πrh = 88
2 × (22/7) × r × 14 = 88
88r = 88 ⇒ r = 1
Diameter = 2 cm.

Q10. The total surface area of a hemisphere of radius 10 cm is (π = 3.14):
(a) 942 cm²
(b) 314 cm²
(c) 628 cm²
(d) 900 cm²
Answer: (a) 942 cm²
Logic: TSA = 3πr² = 3 × 3.14 × 100 = 942.

MENSURATION FORMULA SHEET

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

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 Tip
    Always identify if the question is about:

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

Note: Just learning these formulas will not be effective until you don’t try to implement them in the questions. Don’t worry, we have provided free mensuration tests where you can practice the implementation of the above formulas.

How to Prepare Mensuration Questions for RRB NTPC?

Don’t let formulas haunt you. Follow these simple steps to master this topic:

• The Wall Chart Method: Write all the formulas (especially for Cylinder, Cone, and Sphere) on a large sheet of paper. Stick it in front of your study table. Look at it for 5 minutes every day.
• Visualize the Shape: When the question says “Cylinder,” imagine a Coke can. When it says “Cone,” imagine an ice cream cone. Visualizing helps you understand if you need to calculate Volume (filling it) or Surface Area (painting it).
• Calculation Speed: Mensuration involves a lot of multiplication with 22/7 (π). Practice doing these calculations fast. Often, you can use the “Divisibility by 11” trick to find the answer from the options without solving.
• Attempt Topic Tests: Reading is not enough. You must test your memory. Attempt Free Topic Tests to see if you can recall the correct formula under time pressure.

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