Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
What is the area of the circle ? I. An arc of length 4 cm subtends an angle of 60° at the centre. II. A chord of length 5 cm subtends an angle of 90° at the centre.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
I. Length of $\operatorname{arc}=\frac{2 \pi R \theta}{360} \Leftrightarrow 4=\left(\frac{2 \times \frac{22}{7} \times R \times 60}{360}\right)$. This gives $R$ and therefore, area of the circle $=\pi R^{2}$. Thus, I only gives the answer. II. $R^{2}+R^{2}=5^{2} \Leftrightarrow 2 R^{2}=25 \Leftrightarrow R^{2}=\frac{25}{2}$. ∴ Area of the circle $=\pi R^{2}=\left(\frac{22}{7} \times \frac{25}{2}\right)$ sq. cm.
Explanation as extracted from the printed page; notation may be imperfect.