Mensuration (Railway Maths) (Part – II)

Total Questions: 50

1. Find the area of the parallelogram whose base is 15 cm and the corresponding height is 6 cm. [Group D 24/08/2022 (Morning)]

Correct Answer: (c) 90 cm²
Solution:

Area of parallelogram
= base × height = 15 × 6 = 90 cm²

2. Find the cost of fencing a rectangular plot of land at the rate of ₹30 per meter, whose area is 100 m², and the length of one side is 20 m. [Group D 24/08/2022 (Afternoon)]

Correct Answer: (a) ₹1,500
Solution:

Area of rectangle = 100 m²
Length = 20 m, Breadth = 100 ÷ 20 = 5 m
Perimeter of rectangle
= 2 × (20 + 5) = 2 × 25 = 50 m
Cost of fencing = 50 × 30 = ₹1500

3. The floor of an office has dimensions 5 m x 3 m. The cost of painting the walls and ceiling is ₹7,440 at the rate of ₹60/m². Find the height of the room (in meters). (rounded off to one decimal place) [Group D 24/08/2022 (Evening)]

Correct Answer: (d) 6.8
Solution:

Area of walls and ceiling
= 7440/ 60 = 124 m²
Area of four walls + area of ceiling = 124
⇒ 2 × (5 + 3) × height + 5 × 3 = 124
⇒ 16 × height = 124 - 15
⇒ 16h = 109 ⇒ h = 6.8 m

4. A cube made of edge 18 m is completely filled with milk. The milk is transferred into a cuboid of length 27 m and height 7 m. The width of the cuboid is: [Group D 25/08/2022 (Morning)]

Correct Answer: (d) 30.8 m
Solution:

5. How many cylinders of radius 10 cm and height 20 cm can be filled with water from a cylinder of radius 20 cm and height 100 cm full of water? [Group D 25/08/2022 (Afternoon)]

Correct Answer: (a) 20
Solution:

6. The radius and height of a cylinder are in the ratio 2 : 1. Find its total surface area if the curved surface area is 616 m². [Group D 25/08/2022 (Afternoon)]

Correct Answer: (b) 1848 m²
Solution:

7. Find the volume of a cuboid whose length is 12 m, breadth is 10 m, and height is 15 m. [Group D 25/08/2022 (Evening)]

Correct Answer: (b) 1800 m²
Solution:

Volume of cuboid = length × breadth × height
= 12 × 10 × 15 = 1800 m³

8. A parallelogram has one parallel side length of 12 cm and perpendicular distance between its base and other parallel side is 8 cm. Its area is: [Group D 25/08/2022 (Evening)]

Correct Answer: (a) 96 cm²
Solution:

Area of parallelogram = base × perpendicular distance
= 12 × 8 ⇒ 96 cm²

9. Find the total surface area of a closed cuboid whose length, breadth, and height are 16 cm, 12 cm, and 8 cm, respectively. [Group D 26/08/2022 (Morning)]

Correct Answer: (c) 832 cm²
Solution:

Total surface area of cuboid
= 2(lb + bh + hl)
⇒ 2(16 × 12 + 12 × 8 + 8 × 16)
⇒ 2(192 + 96 + 128) = 2 × 416 = 832 cm²

10. In a trapezium field, PQRS, PQ || RS, PQ = 12m, RS = 22m, distance between PQ and RS is 14m. In this, two crops are to be sown in equal areas. Find the area available for each crop. [Group D 26/08/2022 (Afternoon)]

Correct Answer: (a) 119 m²
Solution: