(IGP) IAS Pre Paper - 2: GS - Basic Numeracy - Volume & Surface Area of Solid Figures (MCQ -16)

1. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls, the volume of the hall is:
(a) 720
(b) 800
(c) 1200
(d) 2000

2.The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5Ö5 cm. It surface area is:
(a) 127 cm²
(b) 236 cm²
(c) 361 cm²
(d) 480 cm²

3. A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:
(a) 309 m³
(b) 270 m³
(c) 360 m³
(d) 607 m³

4.A metallic sheet is of rectangular shape with dimensions 48m× 36m. Fromeach of its corners, a square is cut off so as to make an open box. IfRs. the length of the square is 8 m, the volume of the box (in m³) is:
(a) 5835
Rs.(b) 6400
(c) 6420
(d) 9260

5.An open box is made of wood 3 cm thick. Its external dimensions are 1.46 m, 1.16 m and 8.3 dm. The cost of painting the inner surface of the box at 50 paise per 100 sqr cm is:
(a) Rs. 140
(b) Rs. 277
(c) Rs. 415.50
(d) Rs. 650

6. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6m by 1.1 in and its walls are 5 cm thick. The thickness of the bottom is:
(a) 90 cm
(b) 1 cm
(c) 3.5 m
(d) 3.1 m

7. If ametallic cuboidweighs 16 kg, howmuch would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original?
(a) 0.25 kg
(b) 0.50 kg
(c) 3 kg
(d) 2 kg

8. The areas of -the three adjacent faces of a rectangular box whichmeet in a point are known. The product of these areas is equal to:
(a) the volume of the box
(b) twice the volume of the box
(c) the square of the volume of the box
(d) the cube root of the volume of the box

9. If the areas of the three adjacent faces of a cubical  box are 120 cm² 72 cm² and 60 cm²  respectively, then find the volume of the box.
(a) 720 cm³
(b) 564 cm³
(c) 7200 cm³
(d) 650 cm³

10. If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu. cm; then the length of the shortest side is:
(a) 11 cm
(b) 15 cm
(c) 20 cm
(d) 35 cm

11. The perimeter of one face a of cube is 20 cm. Its volume must be:
(a) 125 cm³
(b) 500 cm³
(c) 1000 cm³
(d) 9000 cm³

12.The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, howmuch will it cost to paint outside of a cube having 8 feet each side?
(a) Rs. 945
(b) Rs. 864
(c) Rs. 876
(d) Rs. 1002

13. If the numbers representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be:
(a) 7
(b) 8
(c) 5
(d) 6

14 How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
(a) 13
(b) 110
(c) 1000
(d) 10000

15. A rectangular boxmeasures internally 1.6mlong, 1mbroad and 60 cmdeep. The. number of cubical blocks each of edge 20 cmthat can be packed inside the box is:
(a) 32
(b) 55
(c) 60
(d) 120

16. How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?
(a) 39
(b) 216
(c) 218
(d) 435

17. A cuboidal block of 6 cm × 9 cm × 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be:
(a)6
(b) 11
(c) 24
(d) 32

18. The size of a wooden block is 5 × 10 × 20 cm. How many such blocks will be required to construct a solid wooden cube of minimum size?
(a) 6
(b) 12
(c) 12
(d) None of these

19. Edge of a cube is 5 cm. Find the surface area.
(a) 125 cm²
(b) 150 cm²
(c) 88.66 cm²
(d) 160 cm²

20. Find the length of the longest pole that can be placed in a room 30 m long, 24m broad and 18 m high.
(a) 30 m
(b) 30Ö2 m
(c) 30Ö3 m
(d) 60 m

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