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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
5740  
6080  
3040  
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
240 m  
300 m  
320 m  
480 m

Question 2 Explanation:
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 2^{nd} meeting A has travelled 2x+20060 = 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
Total circumference = 2(x+100) as they were diametrically opposite.
In the 2^{nd} meeting A has travelled 2x+20060 = 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
125%  
100%  
75%  
50% 
Question 3 Explanation:
Area is directly proportional to r^{2}
=> Area is directly proportional to (1.5 r^{2})
=> Area is directly proportional to 2.25r
The area has increased by (2.25 1)x100 = 125%
=> Area is directly proportional to (1.5 r^{2})
=> 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?
2500 cm^{2}  
2025 cm^{2}  
1600 cm^{2}  
None of these 
Question 4 Explanation:
The side of the inner square = 55 â€“ 2 x 5 = 45 cm = 55 2X5 = 45 cm.
The area of the inner square = 45^{2} =2025 cm^{2}
The area of the inner square = 45^{2} =2025 cm^{2}
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
5.74x cm  
5.4x cm
 
5.64x cm  
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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