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Geometry and Mensuration: Level 2 Test 10

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Question 1
In the given figure, AB is diameter of the circle and points C and D are on the circumference such that CAD= 30o and CBA= 70o. What is the measure of ACD?MATHS,WORDPANDIT,SSC,CAT,BANKPO,
A
40o
B
50o
C
30o
D
90o
Question 1 Explanation: 
CAt, bankpo,ssc,
Question 2
The length of a rectangular field is double its width. Inside the field, there is a square-shaped pond 8 m long. If the area of the pond is 1/8 of the area of the field, what is the length of the field?
A
32 m
B
16 m
C
64 m
D
20 m
Question 2 Explanation: 
The area of the pond = 8X8 = 64 sq. m.
The area of the field = 8 X 64 = 512 sq. m.
The length = $\left\{ 2\times \sqrt{\left( \frac{512}{2} \right)} \right\}=32$
The correct option is (a).
Question 3
Two small circular parks of diameters 16 m, 12 m are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park occupies the same space as the two small parks?
A
10m
B
20m
C
15m
D
25m
Question 3 Explanation: 
The area of the smaller parks = Π82+ Π62 = 22/7(100)
Πr2 =100
r = 10
Question 4
A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marbles tiles 20 cm x 20 cm, find the number of tiles required to cover the path.
A
1800
B
2000
C
200
D
2150
Question 4 Explanation: 
The area of the path = (24+2x1)(14+2x1) -24x14 = 80 sq. m.
The total number of times = (80 x 10000)/400 = 2000
The correct option is (b)
Question 5
A rectangular plate is of 6 m breadth and 12 m length. Two apertures of 2 m diameter each and one aperture of 1 m diameter have been made with the help of a gas cutter. What is the area of the remaining portion of the plate?
A
68.5 sq. m
B
62.5 sq. m
C
65 sq. m
D
None of these
Question 5 Explanation: 
The area of the plate = 12x6 = 72 sq. m.
The total area of the triangle = Π x 12x 2 + Π x 0.52
= (2+0.25)Π = 2.25Π = 7.07 m2
Remaining area = 72 -7.07  = 64.9
Closest option is (c)
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