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Geometry and Mensuration: Test 5

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Question 1
The length of a rectangular floor is twice its breadth. If Rs.256 is required to paint the floor at the rate of Rs.2 per square meters, then what would be the length of floor?
A
16 metres
B
8 metres
C
12 metres
D
32 metres
Question 1 Explanation: 
Let the length be 2x units and breadth = x units.
Area = 256/2 =128 = 2x2
So breadth x= 8 and length = 16 units .
Correct option is (a)
Question 2
The circumference of two circles Is 132 metres and 176 metres respectively. What Is the difference between the area of the larger circle and the smaller circle?
A
1048 sq. metres
B
1076 eq. metres
C
1078 sq. metres
D
1090 sq. metres
Question 2 Explanation: 
$ \displaystyle \begin{array}{l}Let\text{ }the\text{ }radius\text{ }of\text{ }larger\text{ }circle\text{ }be\text{ }R\text{ }m\\and\text{ }smaller\text{ }circle\text{ }be\text{ }r\text{ }m.~\\2\pi r=132\\=>r=21\\and\,2\pi r=176\\=>r=28m\\Difference\text{ }between\text{ }the\text{ }areas\\\frac{22}{7}\times ({{28}^{2}}-{{21}^{2}})\\=49\times 22=1078{{m}^{2}}~~~~~~~~~~~\end{array}$
Question 3
What would be the cost of building a fence around a circular field with area equal to 32378.5 sq. metres, if the price per metre for building the fence was Rs.154?
A
Rs.84, 683
B
Rs.86, 495
C
Rs.79, 326
D
Rs.98, 252
Question 3 Explanation: 
$ \begin{array}{l}\pi {{r}^{2}}=32378.5\\=>r=101.52\\2\pi r=2\times \frac{22}{7}\times 101.5\\=637.74\\Total\,\,\cos t\,=637.74\times 154=98212\end{array}$
Question 4
The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm, and breadth 7 cm. What is the perimeter of a semicircle whose diameter is equal to the side of the square? (Rounded off to the two decimal places)
A
38.57 cms.
B
23.57 cms.
C
42.46 cms.
D
47.47 cms.
Question 4 Explanation: 
Perimeter of the rectangle = 2(8+7) = 30 cm.
Perimeter of square = 30 X 2 = 60 cm.
Side of the square = 60/4 = 15 cm.
Radius of semicircle = 7.5 cm.
Perimeter of semicircle
$ \pi r+2r=\frac{22}{7}\times 7.5+15=23.57+15=38.57cm$
Question 5
The perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is 240 sq. cm. What is the area of the square?
A
100 sq. cm.
B
36 sq. cm.
C
81 sq. cm.
D
Cannot be determined
Question 5 Explanation: 
Nothing is mentioned about length or breadth of the rectangle.
Thus the area of square cannot be determined. Correct option is (d)
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