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Geometry and Mensuration: Level 1 Test 9

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Question 1
The number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm, required to construct a wall 6 m long, 5 m high and 0.5 m thick, while the mortar occupies 5% of the volume of the wall, is
A
5740
B
6080
C
3040
D
8120
Question 1 Explanation: 
$ \displaystyle Total\text{ }number\text{ }of\text{ }bricks\text{ }required\text{ }=\frac{600\times 500\times 50\times 0.95}{25\times 12.5\times 7.5}=6080$
Question 2
A and B travel around a circular path at uniform speeds in opposite directions, starting from diametrically opposite points, at the same time. They meet each other first after B has travelled 100 metres and meet again 60 metres before A completed one round. The circumference of the park is
A
240 m
B
300 m
C
320 m
D
480 m
Question 2 Explanation: 
79 Let A travel x m in the first meeting and thus the ratio of speeds of A and B is x/100.
Total circumference = 2(x+100) as they were diametrically opposite.
In the 2nd meeting A has travelled 2x+200-60 = 2x+140.
B has travelled = 100+x+60 = 160+x,
Ratio of speed A:B = 2x+140/160+x
Equating the two ratios we will get,
x= 140.
Thus the circumference = 2X140+200 = 480 m
Question 3
If the radius of circle is increased by 50%, then the area of the circle is increased by
A
125%
B
100%
C
75%
D
50%
Question 3 Explanation: 
Area is directly proportional to r2
=> Area is directly proportional to (1.5 r2)
=> Area is directly proportional to 2.25r
The area has increased by (2.25 -1)x100 = 125%
Question 4
Four sheets 50 cm x 5 cm are arranged without overlapping to form a square having side 55 cm. What is the area of inner square so formed?
A
2500 cm2
B
2025 cm2
C
1600 cm2
D
None of these
Question 4 Explanation: 
The side of the inner square = 55 – 2 x 5 = 45 cm = 55 -2X5 = 45 cm.
The area of the inner square = 452 =2025 cm2
Question 5
A photo measures 0.9 x cm by 0.94 x cm. It is to be enlarged so that the larger dimension will be 6 cm. The length of the enlarged shorter dimension will be
A
5.74x cm
B
5.4x cm
C
5.64x cm
D
7.09x cm
Question 5 Explanation: 
$latex \displaystyle The\text{ }required\text{ }length=\frac{0.9\times 6}{0.94}=5.74$
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