Quantitative Ability 14
Mensuration - 2D and 3D
CEX-5626/20
Number'of Questions : 25
5. In the following figure, if two lines in the circle
2D Figures intersect at the center of the circle making
the
an angle of 30°, then what fraction of
1. The ratio between the length and the breadth circular area is shaded?
of arectangular field is 5:4. If the breadth is
20 m less than the length, then what is the
perimeter of the field?
(a) 100 m (b) 360 m
(c) 400 m (d) 720 m
30°
2. A circular grass lawn of 28 m radius, has a
path of 14 m wide running around it on the
5 1
outside. What is the area of the path? (b)
(a) 12 12
(a) 3920 m² (b) 3,080 m²
(c) 3980 m² (d) 8,030 m² 1 7
(c) 4
(d) 12
3. Awire bent in the form of a square, encloses
an area of 484cm². If the same wire is 6. A square carpet with an area 196 m², must
bent to form a circle, then the area enclosed have 3 m cut off from one of its edges in order
will be to be pefect fit for a rectangular room. What
(a) 700 cm2 (b)616 cm2 is the area of the rectangular room?
(c) 516 cm² (d) 784 cm² (a)187 m² (b) 184 m²
(c) 160 m² (d) 154 m²
4. How many turns will a wheel of a car rotate in
7. What is the length of the side of the square
a journey of 88 km, if the radius of the wheel
inscribed in a circle of circumference 120 cm?
is 56 cm?
(a)60,000 (b) 50,000 120/2 60V2
(c) 30,000 (d) 25,000 (a) cm (b) cm
601 1201
cm cm
(c) 2 (d)
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8. Afield is in the shape of isosceles trapezium 14. 2cubes each of volume 125 cm are joined
whose parallel sides are 22 m and 10 m. The endtoend. Find the numerical sum of volume
non-parallel sides are 12 meach.The area of and total surface area of the resulting cuboid.
the field (in sq. metres) is. (a) 500 (b) 250
(c) 750 (d) None of these
(a) 64/3 (b) 80/3
(c) 96/3 (d) 112/3 15. Asolid toy is in the form of a hemisphere
surmounted by a right circular cone. The
height of the cone is 5 cm and the radius of
3D Figures
the base is 7 cm. If a right circular cylinder
9 What is the approximate length of the has same radius and height as the toy. The
longest rod that can be placed in a room difference of the volumes of the cylinder and
27 m x 8 m x 1 m? the toy
(a)606 cm (b) 616 cm
(a) 42/4 m (b) 5 m (c) 556 cm3 (d) None of these
(c) /794 m (d) 35 m
2D and 3D Figures
10. A
cylinder, a hemisphere and a cone stand
on the same base and have the same heights. 16. Arectangular plot 80 m x 60 m, has a path of
Find the ratio of their curved surtace area. grass inside it. If the area of the grassy
(b) 1: V2 :1 pathway is 1,300 m², find the width of the
(a) J2:/2:1
path.
(c) V2 :2:1 (d) 1:2:3 (a) 5 m (b) 65 m
(c) 60 m (d) 20 m
11. A copper sphere of radius 6 cm is beaten
and drawn into a wire of diameter 0.8 cm.
17. The side of a cube is x. A new cube is formed
What is the length of the wire?
(a) 100 m (b) 36 m by taking the diagonal as one of its side.
(d) 18 m What is the ratio of surface area of the new
(c) 180 m
cube to that of the original cube?
12. Cost of cOvering 4 walls of a room with paper (a) 3:1 (b) 1:3
is 480. The length, breadth and height of (c) 2:3 (d) 3:2
another room is double that of this room.
What shall be the cost of covering the walls 18. The area of arectangle of width 2 cm is equal
of the room? to the area of a right-angled triangle of sides
(a) 960 (b)7 1,440 5, 12 and 13 cm. What is the length of the
(c) 2,400 (d) ? 1,920 rectangle?
(a) 20 cm (b) 10 cm
13. Ahole is made in a solid cylinder of (c) 15 cm (d) 5 cm
radius 10 cm and length 1,000 cm to obtain
acylindrical shell (hollow cylinder) of uniform
thickness and havingan intenal volume equal 19. The perimeter of a rectangle is 16 cm.
to one-fourth of the volume of the original solid Determine the maximum area satisfying this
cylinder. The thickness of the shell is condition.
(a) 10 cm² (b) 16 cm2
(a) 5(/5 -2)cm (b) 5(2- V3 )cm (c) 25 cm² (d) 36 cm²
(c) 5 cm (d) 5/2 cm
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r is melted and
20. A hollow cylindrical tube that open at both 23. If a solid sphere of radius
find the radius
ends is made of iron 2.5 cm thick. If the cast into a cone of height r,
external diameter is 28 cm and the length of R' of the cone.
(a) R= 2r (b) r= 2R
the tube is 70cm, find the volume of iron in it.
(c) R=3r (d) r= R
(a) 16,048 cm3 (b) 15,000 cm3
(c) 17,092 cm3 (d) 14,025 cm3 square is
24. If the area of a circle inscribed in a
9T cm² then the area of the square is
21. Find the number of smal cubes with edge (a) 24 cm² (b) 30 cm2
10cm that can be accommodated in a cubical (c) 36 cm² (d) 81 cm2
box of 1 m edge.
(a) 100 (b)1,000 25. A5 cm cube is cut into as many 1 cm cubes
surface
(c) 10,000 (d) 5,000 as possible. What is the ratio of the
area of the original cube to that of the sum of
the surface area of the smaller cubes.
22. A solid metal ball of radius 8 cm is melted
and cast into smaller balls, each of radius (a) 2:3 (b) 1:5
2 cm. Find the number of balls thus formed. (c) 2:7 (d) 1:8
(a) 8 (b) 36
(c) 64 (d) 512
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