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Geometry and Mensuration: Level 1 Test 8
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Question 1 
A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangular boxes of dimensions 8 cm x 7 cm x 6 cm. The maximum number of boxes that can be carried in the wooden box is
9800000  
1000000  
7500000  
1200000

Question 1 Explanation:
The dimensions are the same for the wooden box and the rectangular boxes, thus they are similar.
The units are in the ratio of 100:1.
Thus the maximum number of boxes= 100^{3}=1000000
The units are in the ratio of 100:1.
Thus the maximum number of boxes= 100^{3}=1000000
Question 2 
The surface of water in a swimming pool forms a rectangle with length 40m and breadth 15 m. The depth of water increases uniformly from 1.2m to 2.4m at the other end. The volume (in m3) of water in the pool is
500  
540  
720  
1080 
Question 2 Explanation:
A cross section of the pond would look like a trapezium.
The area of the trapezium is Â½ (1.2+2.4) x 40
Thus the total volume of the pond is
= Â½ (1.2+2.4)X40X15 = (600 x 3.6)/2 =1080m^{3}
The area of the trapezium is Â½ (1.2+2.4) x 40
Thus the total volume of the pond is
= Â½ (1.2+2.4)X40X15 = (600 x 3.6)/2 =1080m^{3}
Question 3 
How many litres of water flows out of a pipe of crosssection 5 cm^{ 2} in 1 min. If the speed of water in the pipe is 20 cm/s ?
2 L
 
5 L  
6 L  
9 L 
Question 3 Explanation:
The volume of water flowing = 20 x 60 x 5 = 6000 cm^{3}
Question 4 
The line AB is 6 metres in length and is tangent to the inner one of the two concentric circles at points C. It is known that the radii of the two circles are integers. The radius of the outer circle is
5 m  
4 m  
6 m  
3 m

Question 4 Explanation:
BC= 3 cm
If the center is O then,OC^{2}+BC^{2}=OB^{2} i.e 3^{2} +OC^{2}=OB^{2}
Thus the smallest integers which satisfy the equation s 3,4,5 resp.
Thus the radius of the outer circle = 5 cm
If the center is O then,OC^{2}+BC^{2}=OB^{2} i.e 3^{2} +OC^{2}=OB^{2}
Thus the smallest integers which satisfy the equation s 3,4,5 resp.
Thus the radius of the outer circle = 5 cm
Question 5 
2 cm of rain has fallen on a 1 sq km of land. Assuming that 50% of raindrops could have been collected and contained in a pool having a 100 m x 10 m base, by what level would the water level in the pool have increased?
15 m  
20 m  
10 m  
25 m 
Question 5 Explanation:
50% of 2 cm = 1 cm of rain over 1 sq. km has been collected.
Thus 1000 x 1000 x 0.01 = 10,000 mÂ³ of rain has been collected.
Base area of pond = 1000 m^{2}
The rise = 10000/1000 = 10 m
Thus 1000 x 1000 x 0.01 = 10,000 mÂ³ of rain has been collected.
Base area of pond = 1000 m^{2}
The rise = 10000/1000 = 10 m
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