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 ?

24 + 8\(\Pi \) cm

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.