Mensuration questions for CLAT are an important part of the exam. These questions test your understanding of shapes and their measurements. Knowing the formulas for area, perimeter, volume, and surface area is crucial.
Mensuration questions for competitive exams like CLAT can be tricky, but with practice, you can master them. Let’s understand the key concepts, useful tips, and top practice questions to improve your skills.
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Mensuration Questions for CLAT and Competitive Exams
Let’s practice the top mensuration problems from CLAT previous year question papers:
Passage 1:
The premises of a bank are to be renovated. The renovation is in terms of flooring. Certain areas are to be floored either with marble or wood. All rooms/halls and pantry are rectangular. The area to be renovated comprises of a hall for customer transaction measuring 23 m by 29 m, branch manager’s room measuring 13 m by 17 m, a pantry measuring 14 m by 13 m, a record keeping cum server room measuring 21m by 13 m and locker area measuring 29 m by 21 m. The total area of the bank is 2000 square meters. The cost of wooden flooring is Rs 170/- per square meter and the cost of marble flooring is Rs 190/- per square meter. The locker area, record keeping cum server room and pantry are to be floored with marble. The branch manager’s room and the hall for customer transaction are to be floored with wood. No other area is to be renovated in terms of flooring.
Q1. What is the respective ratio of the total cost of wooden flooring to the total cost of marble flooring?
(a) 1879 : 2527
(b) 1887 : 2386
(c) 1887 : 2527
(d) 1829 : 2527
Q2. If the four walls and ceiling of the branch managers room (the height of the room is 12 meters) are to be painted at the cost of Rs 190/- per square meter, how much will be the total cost of renovation of the branch manager’s room including the cost of flooring?
(a) Rs 1,36,800/-
(b) Rs 2,16,660/-
(c) Rs 1,78,790/-
(d) None of the these
Q3. If the remaining area of the bank is to be carpeted at the rate of Rs 110/- per square meter, how much will be the increment in the total cost of renovation of bank premises?
(a) Rs 5,820/-
(b) Rs 4,848/-
(c) Rs 3,689/-
(d) None of these
Q4. What is the percentage area of the bank that is not to be renovated?
(a) 2.2%
(b) 2.4%
(c) 4.2%
(d) 4.4%
Q5. What is the total cost of renovation of the hall for customer transaction and the locker area?
(a) Rs 2,29,100/-
(b) Rs 2,30,206/-
(c) Rs 2,16,920/-
(d) Rs 2,42,440/-
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Passage 2:
A cuboidal hall has been painted at the rate of Rs. 8 per m2. After painting the hall, cylindrical boxes of radius 0.9 m have been kept in the hall. The total number of boxes kept in the hall is 630 and after keeping all the boxes, there 64.35 m3 of the volume remains vacant. An amount of Rs. 2349 has been incurred for paving the floor of the hall with marbles at the rate Rs. 9 per m2. The length and the breadth of each marble is 90 cm and 50 cm, respectively. The perimeter of the floor of the hall is 65 m. The ratio of the height of the hall to the height of the cylindrical box is 44:7, respectively.
Q6. Find the difference between the length and the breadth of the hall.
(a) 3.5 m
(b) 1.5 km
(c) 7, 5 km
(d) 9.5 km
Q7. Find the number of marbles required to pave the floor.
(a) 560
(b) 580
(c) 520
(d) 640
Q8. Find the cost of painting the hall.
(a) Rs. 7909
(b) Rs. 7340
(c) Rs. 7320
(d) Rs. 7808
Q9. Find the total surface area of one cylindrical box?
(a) 2.97
(b) 4.77
(c) 3
(d) 6.75
Q10. Find the ratio of base Area of cylindrical box and the area covered by marbles?
(a) 198/35
(b) 35/198
(c) 200/47
(d) None of these
Passage 3:
The following table represents information regarding six different fields.
Q11. If total cost of flooring of field A is Rs. 15400 and total cost of flooring of field D is Rs. 5760, find the respective ratio of total cost of fencing of field A and total cost of fencing of field D.
(a) 2 : 3
(b) 5 : 8
(c) 3 : 5
(d) Cannot be determined
Q12. If total cost of flooring of field B is Rs. 34650 and total cost of flooring of field E is Rs. 12600, cost of flooring/m2 of field B is what percent of the cost of flooring/m2 of field E?
(a) 110%
(b) 125%
(c) 75%
(d) 100%
Q13. Total cost of flooring of field F is Rs. 15000 and measure of another pair of parallel sides of field F is 24m. Cost of fencing/m of field C is Rs. 12/m. Find the average of the cost of fencing of field C and cost of fencing of field F.
(a) Rs. 986
(b) Rs. 1020
(c) Rs. 1148
(d) Rs. 1116
Q14. Find the relation between following two quantities.
Quantity I: If cost of fencing field A is Rs. 920, find the total cost of flooring of field A.
Quantity II: Field G is circular in shape and its radius is 7 m more than the radius of field B. If cost of flooring/m2 of field G is Rs. 8, find the total cost of flooring of field G.
(a) Quantity I > Quantity II
(b) Quantity I < Quantity II
(c) Quantity I ≥ Quantity II
(d) Quantity I ≤ Quantity II
Q15. Find the total cost of flooring of field H.
Statement I: Field H is rectangular in shape. Total cost of fencing of field H is Rs. 960.
Statement II: Length of field H is 4 m more than its breadth. Cost of flooring/m2 of field H is Rs. 22. Cost of fencing/m of field H is Rs. 15.
- Statement I alone is sufficient to answer the question, but the statement II alone is not sufficient.
- Statement II alone is sufficient to answer the question, but the statement I alone is not sufficient.
- Either statement I alone or statement II alone is sufficient to answer the question.
- Both statements I and II together are needed to answer the question.
Passage 4:
The premises of a school are to be renovated. The renovation is in terms of flooring. Certain areas are to be floored either with marble or wood. All rooms/halls and pantry are rectangular. The area to be renovated comprises a hall for students’ fee transaction measuring 28m by 32 metres, the branch principal’s room measuring 15m by 18m, a pantry measuring 20m × 14 metres, a record keeping cum server room measuring 23m by 17 metres and staff room 33m by 29 metres. The total area of the school is 3500m2. The cost of wooden flooring is Rs. 160 per m2 and the cost of marble flooring is Rs. 180 per m2. The staff room area, record keeping cum server room and pantry are to be floored with marble. The branch principal’s room and the hall for students fee transaction are with floored to be wood. No other area is to be renovated in terms of flooring.
Q16. What is the ratio of the total cost of wooden flooring to the total cost of marble flooring?
(a) 359 : 471
(b) 213 : 363
(c) 537 : 239
(d) 212 : 333
Q17. If the four walls and ceiling of the principal’s room (the height of the room is 15 metres) are to be painted at the cost of? 175 per square metre, how much will be the total cost of renovation of the principal’s room including flooring?
(a) Rs. 243450
(b) Rs. 263700
(c) Rs. 316590
(d) Rs. 215600
Q18. If the remaining area of the school is to be carpeted at the rate of ₹125 per square metre, how much will the increase in the total cost of renovation of school premises be?
(a) Rs.72189
(b) Rs.658050
(c) Rs.88250
(d) Rs.489560
Q19. What is the total cost of flooring of the hall for students’ fee transaction and staff room area?
(a) Rs. 428969
(b) Rs. 375690
(c) Rs. 528640
(d) Rs. 315620
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Tips and Tricks to Solve Mensuration Problems
Learn and Memorize Key Formulas
Keep a list of essential formulas for 2D and 3D shapes handy. Practice them regularly to ensure they are at your fingertips during exams.
Break Down Complex Shapes
If a problem involves a complex shape, try to break it down into simpler shapes like squares, rectangles, and triangles. Calculate the area, perimeter, or volume for each simple shape, then combine them as required.
Understand the Question Carefully
Read the question thoroughly to understand what is being asked. Identify whether you need to find the area, perimeter, volume, or surface area.
Use Approximation Techniques
For quick calculations, use approximations for values like π (e.g., 3.14 or 22/7). This can help save time during the exam.
Practice Visualization
Visualize the shape in your mind or draw it on paper to better understand the problem. This can help in breaking down complex problems and applying the correct formulas.
Check Units Consistently
Ensure that all measurements are in the same units before performing any calculations. Convert units if necessary to avoid errors.
Simplify Your Calculations
Look for ways to simplify calculations by factoring out common terms. Use basic arithmetic tricks to speed up your work.
Use Diagrams
Draw neat and labeled diagrams whenever possible. This helps in visualizing the problem and keeps your calculations organized.
Review Common Pitfalls
Be aware of common mistakes like confusing diameter with radius, or using the wrong height in volume calculations. Double-check your work to avoid these errors.
Practice Regularly
The more you practice, the better you become at solving mensuration problems quickly and accurately. Use a variety of problems to cover all possible types of questions.
Time Management
Practice solving problems under timed conditions to improve your speed. Allocate specific time slots for different types of mensuration problems during your preparation.
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Free Resources for CLAT Preparation
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| CLAT Current Affairs | CLAT Previous Year Papers |
| CLAT Legal Updates | CLAT Express Magazine |
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Wrapping Up:
Mastering mensuration questions is crucial for success in the CLAT exam. By understanding basic concepts, memorizing key formulas, and practicing regularly, you can tackle these questions with confidence. Remember, consistent practice is key.
Consider taking CLAT mock tests to level up your preparation and identify areas for improvement. Additionally, online CLAT coaching can provide structured guidance and personalized support to enhance your skills.