Three circles of radius 4 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string ?
Answer & explanation
Correct answer: option 1
The length of the string not in contact with the circle = 2r + 2r + 2r
⇒ 6r = 6 x 4 = 24
As we can say the angle covered by the string is \({120}^\circ\)
Or we can say it covered \(\frac{1}{3}\) part of the circle
Length of string touching circle = 2\(\Pi \)/3 + 2\(\Pi \)/3 + 2\(\Pi \)/3
⇒ 2\(\Pi \)/r = 2 x 4 x \(\Pi \)
⇒ 8\(\Pi \)
Total length = 24 + 8\(\Pi \) cm.
Therefore, the answer is 24 + 8\(\Pi \) cm.