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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
A
9800000
B
1000000
C
7500000
D
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= 1003=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
A
500
B
540
C
720
D
1080
Question 2 Explanation: 
A cross section of the pond would look like a trapezium.
The area of the trapezium is ½ (1.2+2.4) x 40
Thus the total volume of the pond is
= ½ (1.2+2.4)X40X15 = (600 x 3.6)/2 =1080m3
Question 3
How many litres of water flows out of a pipe of cross-section 5 cm 2 in 1 min. If the speed of water in the pipe is 20 cm/s ?
A
2 L
B
5 L
C
6 L
D
9 L
Question 3 Explanation: 
The volume of water flowing = 20 x 60 x 5 = 6000 cm3
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
A
5 m
B
4 m
C
6 m
D
3 m
Question 4 Explanation: 
BC= 3 cm
If the center is O then,OC2+BC2=OB2 i.e 32 +OC2=OB2
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?
A
15 m
B
20 m
C
10 m
D
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 m³ of rain has been collected.
Base area of pond = 1000 m2
The rise = 10000/1000 = 10 m
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