Subject: General Aptitude · Chapter: Area · Exam: 2008 · Marks: · Difficulty:
A circular pond has area equal to $616 \mathrm{m}^{2}$. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present?
(a)454 sq. m
(b)462 sq. m
(c)532 sq. m
(d)564 sq. m
Answer
Answer (as printed): B
Explanation
Let the radius of the pond be $R$ metres. Then, $\pi R^{2}=616 \Rightarrow R^{2}=\frac{616 \times 7}{22}=196 \Rightarrow R=14 \mathrm{m}$. Radius of the stage $=\left(\frac{14}{2}\right) \mathrm{m}=7 \mathrm{m}$. ∴ Area where water is present $$=\pi\left(14^{2}-7^{2}\right)=\left(\frac{22}{7} \times 21 \times 7\right) \mathrm{m}^{2}=462 \mathrm{m}^{2} .$$