Mensuration (Railway Maths) (Part – VI)

Total Questions: 50

11. The area of triangle ABC is 39 cm². D and E are two points on BC such that BD = DE = EC, then what is the area of triangle ADC? [RRB NTPC 08/01/2021 (Morning)]

Correct Answer: (a) 26 cm²
Solution:

12. The diagonal of a square is √200 cm. The sides of a rectangle are in the ratio 5 : 2, which is the same as the area of the square, then what is the length of the rectangle? [RRB NTPC 08/01/2021 (Morning)]

Correct Answer: (b) √250 cm
Solution:

13. The radius of a spherical balloon increases from 5 cm to 10 cm when more air is pumped into it. The ratio of the surface area of the original balloon and that of the inflated balloon is: [RRB NTPC 09/01/2021 (Evening)]

Correct Answer: (b) 1 : 4
Solution:

14. A solid metallic cylinder of base radius 3 cm and height 5 cm is melted into cones each of height 1 cm and base radius 1 mm. How many cones are formed? [RRB NTPC 10/01/2021 (Evening) ]

Correct Answer: (d) 13,500
Solution:

15. The dimensions of a metallic cuboid are 50 cm × 40 cm × 32 cm. The cuboid is melted and recast into a cube. Find the surface area of the cube. [RRB NTPC 11/01/2021 (Morning)]

Correct Answer: (d) 9,600 cm²
Solution:

16. Find the volume of the largest sphere that can be carved out of a cube of side 21 cm. [RRB NTPC 11/01/2021 (Morning)]

Correct Answer: (c) 4851 cm³
Solution:

17. A hollow metallic sphere has an internal and external radius of 3 cm and 5 cm respectively. It is melted and recast as a solid cylinder with radius 7 cm. What is the height of the cylinder? [RRB NTPC 11/01/2021 (Evening)]

Correct Answer: (d) 8/3 cm
Solution:

18. The perimeter of a rhombus is 120 m and the distance between any two parallel sides is 15 m. The area of the rhombus is: [RRB NTPC 12/01/2021 (Morning)]

Correct Answer: (a) 450 m²
Solution:

19. The semicircle of area 1250π cm² is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. The area of the rectangle is. [RRB NTPC 13/01/2021 (Morning)]

Correct Answer: (a) 5000 cm²
Solution:

20. A solid sphere of surface area S, is cut into four equal pieces by two radial planes. The total surface area of all the pieces: [RRB NTPC 13/01/2021 (Morning)]

Correct Answer: (c) becomes 2S
Solution:

When we cut a solid sphere into 4 pieces, Each piece has 2 semicircular areas due to the cut.
Area increase = πR² due to one piece
Total area increased = 4πR² = area of solid sphere,
So, the area becomes 2S if the intial area of sphere = S.