Question
Download Solution PDFThree circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Three circles of radius 6 cm are kept touching each other.
Calculation:
The length of the string not in contact with the circle = 2r + 2r + 2r
⇒ 6r = 6 × 6
⇒ 36
By symmetry, the angles swiped by the string on one circle is 120.
Length of string touching circle = 2πr/3 + 2πr/3 + 2πr/3
⇒ 6πr/3
⇒ 2πr = 2 × 6 × π
⇒ 12π
Total length = 36 + 12π
∴ The required answer is 36 + 12π cm.
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