The ratio of the outer and the inner circumference of a circular path is 7 : 6. If the path is 45 m wide, then what is the radius (in m) of the inner circle?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 270.
Let the radius of the inner circle be r meters
Since the path is 45 m wide, the radius of the outer circle = r + 45
The circumference of a circle = 2πr
The ratio of the outer and inner circumferences is given as 7 : 6
Outer Circumference/Inner Circumference = 7/6
⇒ 2π(r + 45)/2πr = 7/6
⇒ (r + 45)/r = 7/6
⇒ 6(r + 45) = 7r
⇒ 6r + 270 = 7r
⇒ r = 270
Thus, The radius of the inner circle is 270 meters.