 # Quant Quiz on “GEOMETRY” for SSC CGL 2016

1. A horse is tied to a pole fixed at one corner of 30 m × 30 m square field of grass, by means of a 10 m long rope. Find the area of that part of the field, in which the horse can graze.

78.5 sq m
79.5 sq m
76.0 sq m
78.0 sq m

2. From four corners of a square sheet of side 4 cm, four pieces, each in the shape of arc of a circle with radius 2 cm are cut out. The area of the remaining portion is

(8-π)sq cm
(16-4π) sq cm
(16-8π)sq cm
(4-2π) sq cm

3. If the four equal circles of radius 3 cm touch each other externally, then the area of the region bounded by the four circles is

4(9-π) sq cm
9(4-π) sq cm
5(6-π) sq cm
6(5-π) sq cm

4. Three circles of diameter 10 cm each, are bound together by a rubber band, as shown in the figure. The length of the rubber band (in cm), if it is stretched as shown, is

30
30 + 10 π
10 π
77
Solution:

Length of rubber band =3d+2πr
=(30+10π) cm

5. An equilateral triangle of side 6 cm has its corners cut off to form a regular hexagon. Area (in cm2) of this regular hexagon will be

3√3
3√6
6√3
(5√3)/2

6. ABC is an equilateral triangle of side 2 cm. With A, B, C as centres and radius 1 cm three arcs are drawn. The area of the region within the triangle bounded by the three arcs is

(3√3-π/2)cm2
(√3-3π/2)cm2
(√3-π/2)cm2
(π/2-√3)cm2

7. The area of the shaded region in the figure given below is

a
b
c
d

8. The area of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 5 cm and the breadth is less than the length of the side of the square by 3 cm. The perimeter of the rectangle is

17 cm
26 cm
30 cm
34 cm

9. If the areas of a circle and a square are equal, then the ratio of their perimeters is

1 : 1
2 : π
π ∶ 2
√π ∶ 2

10. A circular wire of diameter 42 cm is bent in the form of a rectangle whose sides are in the ratio 6 : 5. The area of the rectangle is. (use π=22/7)

540 cm2
1080 cm2
2160 cm2
4320 cm2

11. A square and an equilateral triangle are drawn on the same base. The ratio of their areas is

2 : 1
1 : 1
√3 ∶ 4
4 : √3

12. There is a rectangular tank of length 180 m and breadth 120 m in a circular field. If the area of the land portion of the field is 40000 m2,what is the radius of the field? (tate π=22/7)

130 m
135 m
140 m
145 m

13. The circumference of a circle is 100 cm. The side of a square inscribed in the circle is

(100√2)/π
(50√2)/π
100/π
50√2

14. The area of the greatest circle inscribed inside a square of side 21 cm is (take π=22/7)

344.5 cm2
364.5 cm2
346.5 cm2
366.5 cm2

15. The length of a rectangular garden is 12 m and its breadth is 5 m. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden

2√30 m
√13 m
13 m
8√15 m

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