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Geometry and Mensuration: Test 30

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Question 1
A grassy field has the shape of an equilateral triangle of side 6m. A horse is tied to one of its vertices with a rope of length 4.2m. The percentage of the total area of the field which is available for grazing is best approximated by
A
50%
B
55%
C
59%
D
62%
Question 1 Explanation: 
cat-geometry-and-mensuration-13-png
cat-geometry-and-mensuration-14-png
Question 2
The areas of two circles are in the ratio 1: 2. If the two circles are bent in the form of squares, what is the ratio of their areas?
A
1: 2
B
1: 3
C
1: √2
D
1: 4
Question 2 Explanation: 
Area of two circles in 1:2 then their perimeter will be in 1:√2 Since the circle is bent to form a square,
so the perimeter of square = circumference of the circle
So perimeters of squares will also be in 1:√2
So area of squares is 1²:(√2)²=1: 2
Correct option is (a)
Question 3
A wall is of the form of a trapezium with height 4m and parallel sides being 3m and 5m. What is the cost of painting the wall, if the rate of painting is Rs.25 per sq m?
A
Rs.240
B
Rs.400
C
Rs.480
D
Rs.800
Question 3 Explanation: 
$ \begin{array}{l}The\text{ }area\text{ }of\text{ }the\text{ }wall=\frac{1}{2}(3+5)4=16\,sq\,m\\The\text{ }total\text{ }cost\text{ }=\text{ }25\times 16=Rs.\text{ }400.\\Correct\text{ }option\text{ }is\text{ }\left( b \right)\end{array}$
Question 4
The area of a rectangle whose length is 5 units more than twice its width is 75 sq units. What is the width?
A
3 units
B
5 units
C
7 units
D
10 units
Question 4 Explanation: 
Let the width of the rectangle be x units and thus length = 2x+5.
Thus, (2x+5)x=75
=>x=5.
Correct option is (b).
Question 5
The diameter of a circle circumscribing a square is 15√2cm. What is the length of the side of the square?
A
15 cm
B
12 cm
C
10 cm
D
7.5 cm
Question 5 Explanation: 
The diameter of the circle = diagonal of the square. Let the side of the square is 'x' cm.
So x2 + x2 = (15√2)2 = 450
=> 2x2 = 450
=> x2 = 225
=> x = 15 cm
Thus the side= 15 cm Correct option is (a)
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