Subject: General Aptitude · Chapter: Area · Exam: 2008 · Marks: · Difficulty:
The area of a circle whose radius is 6 cm, is trisected by two concentric circles. Find the radius of the smallest circle.
Answer
Answer (as printed):
Explanation
Let the radius of the smallest circle be r and that of the middle circle be R. Then, p[62 – R2] = p[R2 – r2] ⇒ 62 – R2 = R2 – r2 ⇒ 2R2 = 36 + r2 36 + r 2 ⇒ R2 = ...(i) 2 And, p[R2 – r2] = pr2 ⇒ R2 – r2 = r2 ⇒ R2 = 2r2 36 + r 2 ⇒ = 2r 2 ⇒ 3r 2 = 36 2 ⇒ r2 = 12 ⇒ r = 12 = 2 3 cm. Hence, radius of the smallest circle = 2 3 cm.
Explanation as extracted from the printed page; notation may be imperfect.