Geometry and Mensuration: Test 5

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These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
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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?