Question : The cost of building a fence around a circular field is INR 7,425 at the rate of INR 13.50 per foot. What is the area of the circular field? [Use $\pi=\frac{22}{7}$]
Option 1: 25018.5 ft2
Option 2: 23864.4 ft2
Option 3: 24644.5 ft2
Option 4: 24062.5 ft2
Correct Answer: 24062.5 ft 2
Solution :
Given,
The cost of building a fence around a circular field is INR 7,425 at the rate of INR 13.50 per foot.
We know that the area of the circular field = $\pi r^2$
And, The circumference of the circular field = $2πr$, where $r$ is the radius
Let the radius of the circular field be '$r$' ft.
⇒ The circumference of the circular field = $2πr$ ft
The cost of building a fence at the rate of INR 13.50 per foot = INR 7,425
⇒ $2πr$ × 13.50 = 7,425
⇒ $2πr$ = $\frac{7425}{13.50}$ = 550
⇒ $πr$ = 275
⇒ $r$ = $\frac{275}{π}$
Now, the area of the circular field = $\pi r^2$
= $π(\frac{275}{π}$)
2
= $π(\frac{275^2}{π^2}$)
= $\frac{275^2}{π}$
= $\frac{275 × 275 × 7}{22}$
= 24062.5 ft
2
Hence, the correct answer is 24062.5 ft
2
.
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