Question : A field is in the form of a circle. The cost of fencing around it at INR 12 per metre is INR 2,640. What is the area (in m2) of the field? (Take $\pi=\frac{22}{7}$)
Option 1: 1,925 m2
Option 2: 3,850 m2
Option 3: 2,772 m2
Option 4: 5,544 m2
Correct Answer: 3,850 m2
Solution : Given: A field is in the form of a circle. Use the formulas, The perimeter of the circle = $2\pi r$, The area of the circle = $\pi r^2$, where $r$ is the radius. The cost of fencing around it at INR 12 per metre is INR 2,640. So, the perimeter of the field = $\frac{2640}{12}$ = 220 m ⇒ $2\pi r =220$ ⇒ $r =\frac{220\times 7}{2\times 22}=35$ m So, the area of the field $=\frac{22}{7}\times {35}^2=3,850$ m2 Hence, the correct answer is 3,850 m2.
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Question : The circumference of a circle exceeds its diameter by 60 cm. The area of the circle is: (Take $\pi=\frac{22}{7}$ )
Option 1: 1078 cm2
Option 2: 616 cm2
Option 3: 536 cm2
Option 4: 346.5 cm2
Question : The sides of a triangular field are 120 m, 170 m and 250 m. The cost of levelling the field at the rate of INR 7.40/m2 is:
Option 1: INR 65,120
Option 2: INR 63,640
Option 3: INR 59,200
Option 4: INR 66,600
Question : The area of a circle is 1386 cm2. What is the radius of the circle? [Use $\pi= \frac{22}{7}$]
Option 1: 7 cm
Option 2: 14 cm
Option 3: 18 cm
Option 4: 21 cm
Question : The perimeter of a sheet of paper in the shape of a quadrant of the circle is 75 cm. Its area would be $(\pi=\frac{22}{7})$
Option 1: 100 cm2
Option 2: 346.5 cm2
Option 3: 693 cm2
Option 4: 512.25 cm2
Question : The cost of painting the total surface area of a 30 m high solid right circular cylinder at the rate of Rs. 25 per m2 is Rs. 18,425. What is the volume (in m3) of this cylinder [use $\pi=\frac{22}{7}$ ]?
Option 1: 1145
Option 2: 1210
Option 3: 1155
Option 4: 1122
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