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Geometry and Mensuration: Level 2 Test 8

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Question 1
In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If length of one chord is 16 cm, then the length of the other is
A
15 cm
B
23 cm
C
30 cm
D
34 cm
Question 1 Explanation: 
98
Let half the length of one chord = 16/2 = 8 cm.
Thus one part of the perpendicular distance of the chord is 15 cm (by Pythagoras theorem)
The other part is 23-15 = 8 cm
Thus half the length of the other chord = 15 cm (by Pythagoras theorem)
Thus the length of the other radius = 2X 15= 30 cm
Correct option is (c)
Question 2
If the area of a square inscribed in a circle is 15 cm2, then the area of the square inscribed in a semicircle of the same circle, in cm2, is
A
5
B
6
C
7.5
D
√50
Question 2 Explanation: 
99
The radius of the circle = (15/2) cm
Let the side of the square be 2x.
Thus (2x)2 = 15/2 –x2
5x2= 15/2
4x2 = 6
The area =  6 sq. m
The correct option is (b)
Question 3
Diameter of a cylindrical jar is increased by 25%, By what percent must the height be decreased so that there is no change in its volume?
A
18%
B
25%
C
32%
D
36%
Question 3 Explanation: 
The diameter is increased by 25% and thus the radius has increased by 25%
i.e. 5/4 of the previous length.
The volume is a function of square of the radius and height.
Thus the height should decrease by 16/25 = 36%.
Question 4
The sides of a triangle are 5, 12 and 13 units. A rectangle is constructed, which is equal in area to the triangle, has a width of 10 units. Then, the perimeter of the rectangle is:
A
30 units
B
36 units
C
13 units
D
None of these
Question 4 Explanation: 
Sides of the triangle = 5,12,13
We can say that it is right angled triangle with length 12 , hypotenuse 13 and height 5
So the area of the triangle = ½ x 12 x 5 = 30
Acc. to question
A rectangle is constructed, which is equal in area to the triangle, has a width of 10 units.
Therefore
Length x 10 = 30
Length = 3
Therefore the perimeter of the triangle = 2(l+b)  = 2(13 ) = 26 units
Question 5
For a triangle, base is 6√3cm and two base angles are 30o and 60o. Then height of the triangle is
A
$ \displaystyle 3\sqrt{3}$
B
$ \displaystyle 4.5$
C
$ \displaystyle 4\sqrt{3}$
D
$ \displaystyle 2\sqrt{3}$
Question 5 Explanation: 
100
Since this is a 30-60-90 triangle the other two sides are 3√3 and 9 cm
Thus the height = (3√3 x 9)/6√3 = 4.5 cm
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