Tips to Master Mensuration for RBI Grade B Exam

Mensuration is a portion of the Quantitative Aptitude section in the RBI Grade B Phase 1 exam. Previous years’ exam analysis says, it does appear in the exam. But it doesn’t mean it is not worth preparing or neglecting, because whenever it shows up, it carries 2 to 3 marks. This topic is about figuring out the area, volume, and surface area of various shapes. It’s actually one of the most complicated sections of Quant, although it seems easy at first. Why? The reason is simple. Candidates need to remember many intricate formulas and use them quickly. Hence, mastering it means maximizing your overall score in the Quantitative Aptitude section. In this blog, we’ll share with you some simple and smart tips to help you solve Mensuration questions accurately. You’ll also find sample questions with methods to sharpen your preparation and accelerate your problem-solving skills.

Tips to Solve Mensuration Questions Quickly

The number of questions dedicated specifically to Mensuration in the RBI Grade B exam is low as compared to other topics like Data Interpretation. For example, the 2023 exam included more questions on topics like Data Interpretation and Number Series than Mensuration. So, you should spend time on Mensuration, but just make sure you don’t ignore the more important topics. You need a versatile preparation strategy that touches on every topic.

Let’s take a look at the best tips to master Mensuration questions:

1. Memorize All Important Formulas by Category

There are plenty of formulas that you’ll have to learn in Mensuration. And, if you forget or try to think hard while solving a question, you’ll just slow your answering process down. Therefore, you need to recall quickly for quicker actions leading to quicker solutions. So, you have to learn them by heart in advance.

Here are some tips:

• Make a list of formulas (for 2D and 3D shapes).
• Divide them into categories like Area, Volume, and Surface Area.
• Use flashcards or charts for daily revision.
• Regularly practice formula-based MCQs.

2. Understand Units and Conversions

Mensuration problems often encompass traps based on units. So, you need to exercise caution whenever you convert units like cm to m or m² to cm².

Here’s what to do:

• Always check the unit in question and options.
• Keep a mental note: 1 m = 100 cm, 1 m² = 10,000 cm².
• Convert before starting the calculation.

Keep in mind that wrong units, even with the right formula, will give you the wrong answer.

3. Break the Shape into Parts

Some questions involve composite shapes like a rectangle with a semicircle or a cone on a cylinder. So, handle each part separately to make it easier.

Let’s break it down:

• Find the area or volume of each section.
• Add or subtract as required.
• Use correct formulas for each shape.
• Try your best to avoid confusion and calculation mistakes.

4. Practice with Diagram-Based Questions

Mensuration questions usually have diagrams, so if you can visualize them, you’ll solve them much quicker.

Try this method:

• Draw simple shapes if they’re not provided.
• Label all sides, radius, and height clearly.
• Find hidden values or overlapping shapes.
• Try to get more accurate and see things more clearly.

5. Improve Speed Through Timed Practice

You’ll get faster and better if you time yourself. So try to practice just like you’re in the real exam.

Here’s how:

• Use a timer (set 1 minute per question).
• Try mixed Mensuration quizzes and RBI Grade B 2025 mock tests.
• Mark the questions you got wrong, and revise the concept.
• This shows you what needs improvement, so you can get better at it.

Sample Mensuration Questions for Practice

Question 1:

A right triangle is rotated about its perpendicular and then by its base such that the ratio of the volume of resulting cones is 3:4. Find the ratio of the volume of the cylinder formed when it is rotated about its right vertex to the sum of the volumes of both cones.

A) 18: 17

B) 36: 35

C) 6: 5

D) 12: 7

Question 2: A board has dimensions 150 cm × 50 cm. The word DETTOL needs to be painted on it such that each letter has a thickness 3.5 cm and can just be enclosed in a square of side 14 cm. Find the cost of painting the letters at Rs. 20 per cm² and background remaining after the letters are painted at Rs. 10 per cm².

A) Rs. 44270

B) Rs. 81387.5

C) Rs. 62675.25

D) Rs. 76435

Question 3: A full tank has an outlet at one-third the height of the tank from the top and another at one-fifth of the tank’s height from the ground. Water flows simultaneously at 34 L/hr and 30 L/hr from the higher and lower outlets respectively. If it takes 186 hours for water to stop flowing from the lower outlet, find the volume of the tank.

A) 3400 L

B) 5100 L

C) 3100 L

D) None of these

Question 4: Radius and the height of a cylinder are in the ratio 3:4 respectively. If the volume of the cylinder is _______ cm³, then the curved surface area of the cylinder is ________ cm² less than the total surface area of the cylinder. (Take π = 3)

The values given in which of the following options will fill the blanks in the same order in which is it given to make the above statement true:

A. 2916, 486

B. 864, 192

C. 6912, 864

D. 13500, 1250

E. 108, 36

A) Only A

B) Only A and C

C) Only B, C and E

D) Only A, C and E

E) Only B and C

Question 5: Curved surface area of a cylinder is 1512 cm².Difference between the radius and slant height of cone is 25 cm, and its curved surface area is 4452 cm². Radius of cylinder is ____ cm and difference between the volume of cone and cylinder is _____cm³. [Take π = 3]

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 18, 21622

II. 30, 12600

III. 42, 3528

A) Only I and III

B) Only III

C) Only II and III

D) Only I

E) Only I and II

प्रश्न 1: A right triangle is rotated about its perpendicular and then by its base such that the ratio of the volume of resulting cones is 3:4. Find the ratio of the volume of the cylinder formed when it is rotated about its right vertex to the sum of the volumes of both cones.

A) 18: 17

B) 36: 35

C) 6: 5

D) 12: 7

प्रश्न 2: A board has dimensions 150 cm × 50 cm. The word DETTOL needs to be painted on it such that each letter has a thickness 3.5 cm and can just be enclosed in a square of side 14 cm. Find the cost of painting the letters at Rs. 20 per cm2 and background remaining after the letters are painted at Rs. 10 per cm2.

A) Rs. 44270

B) Rs. 81387.5

C) Rs. 62675.25

D) Rs. 76435

प्रश्न 3: A full tank has an outlet at one-third the height of the tank from the top and another at one-fifth of the tank’s height from the ground. Water flows simultaneously at 34 L/hr and 30 L/hr from the higher and lower outlets respectively. If it takes 186 hours for water to stop flowing from the lower outlet, find the volume of the tank.

A) 3400 L

B) 5100 L

C) 3100 L

D) None of these

प्रश्न 4: एक बेलन की त्रिज्या और ऊंचाई का अनुपात क्रमशः 3:4 है|यदि बेलन का आयतन _______ cm³ है, तो बेलन का वक्र पृष्ठ का क्षेत्रफल बेलन के सम्पूर्ण पृष्ठ के क्षेत्रफल से ________ cm² है|(Take π = 3)

निम्नलिखित में से किस विकल्प में से दिए गए मान को उसी क्रम में रिक्त स्थान पर भरने पर उपरोक्त कथन सत्य हो जायेगा:

A. 2916, 486

B. 864, 192

C. 6912, 864

D. 13500, 1250

E. 108, 36

A) Only A

B) Only A and C

C) Only B, C and E

D) Only A, C and E

E) Only B and C

प्रश्न 5: एक बेलन के वक्र पृष्ठ का क्षेत्रफल 1512 cm² है|एक शंकु के त्रिज्या और तिरछी ऊंचाई के बीच का अंतर 25 cm है, और इसके वक्र पृष्ठ का क्षेत्रफल 4452 cm² है|बेलन की त्रिज्या ____ cm है और शंकु और बेलन के आयतन के बीच का अंतर _____cm³ है| [Take π = 3]

निम्न में से किस विकल्प में दिए गए मान को उसी क्रम में रिक्त स्थान में भरने पर उपरोक्त कथन सत्य होगा:

I. 18, 21622

II. 30, 12600

III. 42, 3528

A) Only I and III

B) Only III

C) Only II and III

D) Only I

E) Only I and II

ANSWER KEYS and SOLUTIONS:

1) – B)

2) – B)

3) – B)

4) – B)

5) – C)

Solution 1: B)

Solution 2: B)

Solution 3: B)

Solution 4: B)

Let the radius and the height of the cylinder are 3x cm and 4x cm respectively.

So the volume of the cylinder = 3 × (3x)² × 4x = 108x³ cm³

Difference between the curved surface area and the total surface area = 2π(3x)² = 54x² cm²

For option A:

108x³ = 2916

x³ = 27

x = 3

So the difference between the curved surface area and total surface area = 54 × 3² = 486 cm²

So option A can be the answer.

For option B:

108x³ = 864

x³ = 8

x = 2

So the difference between the curved surface area and total surface area = 54 × 2² = 216 cm²

So option B can’t be the answer.

For option C:

108x³ = 6912

x³ = 64

x = 4

So the difference between the curved surface area and total surface area = 54 × 4² = 864 cm²

So option C can be the answer.

For option D:

108x³ = 13500

x³ = 125, x = 5

So the difference between the curved surface area and total surface area = 54 × 5² = 1350 cm²

So option D can’t be the answer.

For option E:

108x³ = 108

x³ = 1, x = 1

So the difference between the curved surface area and total surface area = 54 × 1² = 54 cm²

So option E can’t be the answer.

Hence, option b.

Solution 5: C)

Let, radius and height of cylinder be ‘r’ cm and ‘h’ cm respectively.

Curved surface area of cylinder = 1512

2πrh = 1512

πrh = 756

Volume of cylinder = π × r × r × h = 756r cm³

Let, radius and slant height of cone be ‘x’ cm and ‘x + 25’ cm respectively.

So, 3 × x × (x + 25) = 4452

x² + 25x = 1484

x² + 25x – 1484 = 0

x² + 53x – 28x – 1484 = 0

x(x + 53) – 28(x + 53) = 0

x = 28, -53

Radius of cone = 28 cm

Slant height of cone = 28 + 25 = 53 cm

Height of cone = (53² – 28²)^0.5 = 45 cm

Volume of cone = 1/3 × 3 × 28 × 28 × 45 = 35280 cm³

From option I:

Volume of cylinder = 756 × 18 = 13608 cm³

Volume of cone = 35280 cm³

Difference = 21672 cm³

So, option I cannot be the answer.

From option II:

Volume of cylinder = 756 × 30 = 22680 cm³

Volume of cone = 35280 cm³

Difference = 12600 cm³

So, option II can be the answer.

From option III:

Volume of cylinder = 756 × 42 = 31752 cm³

Volume of cone = 35280 cm³

Difference = 3528 cm³

So, option III can be the answer.

Hence, option c.

Takeaway

Mensuration can be tough at first. Especially because there are a lot of formulas to learn and apply for solutions. But if you have the right tricks and strategies and you practice them regularly, you can master the art of solving all types of questions related to the topic. And it becomes one of the most scoring parts of the Quant section. So, keep revising the formulas, solve an array of problems, and focus on speed and accuracy. Want to improve your marks in Quant? Start your preparation with PracticeMock’s Free RBI Grade B Mock Test and explore expert-level guidance to crack the exam.

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