Mensuration (Part-2)

31. A solid cube of volume 13824 cm³ is cut into 8 cubes of equal volumes. The ratio of the surface area of the original cube to the sum of the surface areas of three of the smaller cubes is: [SSC CGL 04/06/2019 (Morning)]

(a) 2:3
(b) 4:3
(c) 8:3
(d) 2:1

Correct Answer: (b) 4:3

Solution:

32. The unequal side of an isosceles triangle is 2cm. The medians drawn to the equal sides are perpendicular. The area of the triangle is: [SSC CPO 16/03/2019 (Evening)]

(a) 2cm²
(b) 3cm²
(c) 5cm²
(d) 1cm²

Correct Answer: (b) 3cm²

Solution:

33. A steel vessel has a base of length 60 cm and breadth 30 cm. Water is poured in the vessel. A cubical steel box having an edge of 30 cm is immersed completely in the vessel. By how much will the water rise? [SSC CPO 16/03/2019 (Evening)]

(a) 12 cm
(b) 15 cm
(c) 10 cm
(d) 9 cm

Correct Answer: (b) 15 cm

Solution:

34. Original breadth of a rectangular box is 20cm. The box was then remade in such a way that its length increased by 30% but the breadth decreased by 20% and the area increased by 100 cm². What is the new area(in cm²) of the box? [SSC CPO 16/03/2019 (Evening)]

(a) 2500
(b) 2200
(c) 2600
(d) 2400

Correct Answer: (c) 2600

Solution:

35. Find the cost of carpeting a room which is 11m long and 6m broad by a carpet which is 60cm broad at the rate of rs 112.50 per meter. [SSC CPO 16/03/2019 (Afternoon)]

(a) 12,375
(b) 13,280
(c) 11,695
(d) 12,040

Correct Answer: (a) 12,375

Solution:

36. A field is 119m x 18m in dimension. A tank 17m x 6m x 3m is dug out in the middle and the soil removed is evenly spread over the remaining part of the field. The increase in the level on the remaining part of the field is: (in cm) [SSC CPO 16/03/2019 (Afternoon)]

(a) 14 cm
(b) 13 cm
(c) 15 cm
(d) 12 cm

Correct Answer: (c) 15 cm

Solution:

37. A swimming pool is 40 m in length, 30 m in breadth and 2.2 m in depth. The cost of cementing its floor and the four sides at Rs. 25/m² is: [SSC CPO 16/03/2019 (Afternoon)]

(a) Rs.43,980
(b) Rs.37540
(c) Rs.34260
(d) Rs.37700

Correct Answer: (d) Rs.37700

Solution:

38. A square cardboard with side 3 m is folded through one of its diagonal to make a triangle, the height(m) of the triangle is: [SSC CPO 16/03/2019 (Morning)]

Correct Answer: (a)

Solution:

39. If the area of a regular hexagon is 108√3cm², its perimeter (in cm) is: [SSC CPO 15/03/2019 (Evening)]

(a) 36√2
(b) 42√2
(c) 28√3
(d) 24

Correct Answer: (a) 36√2

Solution:

40. A square piece of cardboard with side 12 cm has a small square of 2 cm cut out from each of the corners. The resulting flaps are turned up to make a box 2 cm deep. The volume (in cm³) of the box is: [SSC CPO 15/03/2019 (Evening)]

(a) 128
(b) 94
(c) 102
(d) 11

Correct Answer: (a) 128

Solution:

Mensuration (Part-2)

31. A solid cube of volume 13824 cm³ is cut into 8 cubes of equal volumes. The ratio of the surface area of the original cube to the sum of the surface areas of three of the smaller cubes is: [SSC CGL 04/06/2019 (Morning)]

32. The unequal side of an isosceles triangle is 2cm. The medians drawn to the equal sides are perpendicular. The area of the triangle is: [SSC CPO 16/03/2019 (Evening)]

33. A steel vessel has a base of length 60 cm and breadth 30 cm. Water is poured in the vessel. A cubical steel box having an edge of 30 cm is immersed completely in the vessel. By how much will the water rise? [SSC CPO 16/03/2019 (Evening)]

34. Original breadth of a rectangular box is 20cm. The box was then remade in such a way that its length increased by 30% but the breadth decreased by 20% and the area increased by 100 cm². What is the new area(in cm²) of the box? [SSC CPO 16/03/2019 (Evening)]

35. Find the cost of carpeting a room which is 11m long and 6m broad by a carpet which is 60cm broad at the rate of rs 112.50 per meter. [SSC CPO 16/03/2019 (Afternoon)]

36. A field is 119m x 18m in dimension. A tank 17m x 6m x 3m is dug out in the middle and the soil removed is evenly spread over the remaining part of the field. The increase in the level on the remaining part of the field is: (in cm) [SSC CPO 16/03/2019 (Afternoon)]

37. A swimming pool is 40 m in length, 30 m in breadth and 2.2 m in depth. The cost of cementing its floor and the four sides at Rs. 25/m² is: [SSC CPO 16/03/2019 (Afternoon)]

38. A square cardboard with side 3 m is folded through one of its diagonal to make a triangle, the height(m) of the triangle is: [SSC CPO 16/03/2019 (Morning)]

39. If the area of a regular hexagon is 108√3cm², its perimeter (in cm) is: [SSC CPO 15/03/2019 (Evening)]

40. A square piece of cardboard with side 12 cm has a small square of 2 cm cut out from each of the corners. The resulting flaps are turned up to make a box 2 cm deep. The volume (in cm³) of the box is: [SSC CPO 15/03/2019 (Evening)]

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