Mensuration is an important topic in the quantitative aptitude section of many bank exams. It involves calculating the area, perimeter and volume of various geometric shapes. Knowledge of mensuration is not only essential for competitive exams but is also practical in real-world situations, making it an important subject for banking aspirants. This article covers important formulas and provides example questions to help you practice and excel in the Mensuration section of bank exams.

## Mensuration for Bank Exams

Mensuration is the branch of mathematics that deals with the measurement of length, area and volume of various shapes. In bank exams, questions can range from simple 2D shapes like square and circle to more complex 3D shapes like cylinder and sphere. Being proficient in mensuration requires knowing specific formulas and understanding how to apply them accurately within a time limit.

### Major measurement formula

2D shape

Measurement formula: 2D |
||

size |
Area |
circumference/circumference |
---|---|---|

Social class |
Side^{2} |
4* side |

rectangle |
lb |
2(L+B) |

triangle |
1/2*B*H |
sum of all sides |

circle |
PR^{2} |
2pr |

quadrilateral |
b*h |
2*(B+H) |

trapezium |
1/2 * (sum of parallel sides) * h |
sum of all sides |

3D shape:

Measurement formula: 3D |
||

size |
volume |
surface area |
---|---|---|

cube |
Side^{3} |
6 * side^{2} |

cuboid |
L*B*H |
2 ( L*B + B*H + H*L) |

Cylinder |
Ï€r^{2}h |
2Ï€r (r + h) |

Who? |
1/3 Ï€r^{2}h |
Ï€r (r + slant height) |

Circle |
4/3 Ï€r^{3} |
4Ï€r^{2} |

hemisphere |
2/3 Ï€r^{3} |
Winding: 2Ï€r^{2}Total: 3Ï€r^{2
} |

## Measurement Questions for Bank Exams

**Q1. The diameter of the driving wheel of a bus is 280 cm. How many revolutions per minute must the wheel make to maintain a speed of 66 km per hour? **

(A) 150

(B) 180

(c) 145

(d) 125

(e) none of these

**Q2. Find the ratio of the areas of a square circle and a circumscribed circle. **

(A) 1:2

(B) 3 : 2

(c) 2 :1

(d) 4 :5

(e) none of these

**Q3. A rope is in the shape of a square covering an area of â€‹â€‹44 cm^2. If the same rope is folded in the form of a circle then find the area of â€‹â€‹that circle. **

(a) 40 cm square

(b) 78 cm square

(c) 68 cm square

(d) 52 cm square

(e) 56 cm square

**Q4. The area of â€‹â€‹a rhombus is 144 cm square. One of its diagonals is twice the other. What is the length of the smaller diagonal? **

(a) 12 cm

(b) 11 cm

(c) 10 cm

(d) 14 cm

(e) none of these

**Q5. The base of a parallelogram is twice its height and its area is 128 cm square. find its difference ****Height and base. **

(a) 6 cm

(b) 7 cm

(c) 8 cm

(d) 9 cm

(e) 10 cm

**Q6. If the area of â€‹â€‹the trapezium is 250 square meters then find the distance between two parallel sides of the trapezium. And both parallel sides are equal to 15 meters and 10 meters respectively. **

(a) 25 m

(b) 20 m

(c) 40 m

(d) 30 m

(e) none of these

**Q7. In measuring the sides of a rectangle, one side is taken 5% more and the other 4% less. Find the percentage error in the area calculated from the measurements. **

(A) â€“ 0.5%

(B) 0.8%

(c) 1%

(d) -1%

(e) none of these

**Q8. A rectangular grassy plot of 160 m Ã— 45 m is surrounded by a 2.5 m wide gravel path. Find the cost of laying gravel on the path at the rate of 75 paise per square metre. **

(A) Rs. 650

(B) Rs. 700

(c) Rs. 800

(d) Rs. 750

(e) none of these

**Q9. In the middle of a rectangular lawn of 80 m Ã— 60 m are two roads 10 m wide, one parallel to the length and the other parallel to the width. Find the cost of laying gravel on them in Rs. 30 per square meter. **

(A) Rs. 39950

(B) Rs. 38500

(c) Rs. 39000

(d) Rs. 38000

(e) Rs. 40000

**Q10. The circumference of a circular garden is 1012 metres. Outside the garden, a 3.5 meter wide road runs around it. Find the cost of bridging it at the rate of 50 paise per square metre. **

(A) Rs. 1680

(B) Rs. 1790.25

(c) Rs. 1875.75

(d) Rs. 1750

(e) none of these

**Question 11. Two solid cylinders of radii 4 cm and 5 cm and lengths 6 cm and 4 cm respectively are transformed into cylindrical discs of 1 cm thickness. is the radius of the disk**

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

(e) 32 cm

**Question 12. The diameter of the base of a cylindrical drum is 35 dm and height is 24 dm. It is filled with kerosene. How many tins of size 25 cm Ã— 22 cm Ã— 35 cm can be filled with kerosene from the drum? (Use Ï€=22/7) **

(A) 1200

(B) 1020

(c) 600

(d) 120

(e) 160

**Q13. A path of equal width surrounds a circular park. The difference between the inner and outer circumference of this circular path is 132 meters. Its width is (take Ï€=22/7)**

(a) 22 m

(b) 20 m

(c) 21 m

(d) 24 m

(e) 26 m

**Question 14. A man observed that it takes 30 seconds to cover a circular ground along its diameter once compared to covering it once along its boundary. If its speed was 30 m/min, then the radius of the circular ground is (take Ï€=22/7). **

(a) 10.5 m

(b) 3.5 m

(c) 5.5 m

(d) 7.5 m

(e) 8.5 m

**Question 15. The area of â€‹â€‹a triangle is 216 cm^2 and the ratio of its sides is 3 : 4 : 5. The perimeter of the triangle is **

(a) 6 cm

(b) 12 cm

(c) 36 cm

(d) 72 cm

(e) 24 cm

## Tips to solve mensuration problems in bank exams

**Remember the formula:**Having a solid understanding of the formulas of both 2D and 3D shapes is essential for quick problem-solving.**Practice regularly:**Mensuration questions require consistent practice to ensure speed and accuracy in the exam.**Use estimation:**For tests that do not require exact values, use approximate values â€‹â€‹for pi (â‰ˆ 3.14) to save time.**Understand Units:**Always check the units in question. Converting units where necessary ensures accuracy, especially in volume and surface area problems.**Identify shape properties:**Recognizing properties such as symmetry can simplify calculations, especially in complex shapes.

Solution |
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01 |
D | 02 |
A | 03 |
E | 04 |
A | 05 |
C |

06 |
b | 07 |
b | 08 |
D | 09 |
C | 10 |
b |

11 |
b | 12 |
A | 13 |
C | 14 |
D | 15 |
D |