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 m 2
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 $=\frac{22}{7}\times {35}^2=3,850$ m
2
Hence, the correct answer is 3,850 m
2
.
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