Subject: General Aptitude · Chapter: Area · Exam: 2006 · Marks: · Difficulty:
The perimeter of a circular field and a square field are equal. If the area of the square field is $12100 \mathrm{m}^{2}$, the area of the circular field will be
(a)$15200 \mathrm{m}^{2}$
(b)$15300 \mathrm{m}^{2}$
(c)$15400 \mathrm{m}^{2}$
(d)$15500 \mathrm{m}^{2}$
Answer
Answer (as printed): C
Explanation
Side of the square field $=\sqrt{12100} \mathrm{m}=110 \mathrm{m}$. Perimeter of the circular field = Perimeter of the square field $=(4 \times 110) \mathrm{m}=440 \mathrm{m}$. $$2 \pi R=440 \Rightarrow R=\frac{440 \times 7}{2 \times 22}=70 \mathrm{m} .$$ ∴ Area of the circular field $=\left(\frac{22}{7} \times 70 \times 70\right) \mathrm{m}^{2}=15400 \mathrm{m}^{2}$