Question : Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Option 1: $42 + 7\pi\ ext{cm}$
Option 2: $21\pi + 14\ ext{cm}$
Option 3: $42 + 14\pi\ ext{cm}$
Option 4: $7 + 14\pi\ ext{cm}$

Question

Question : Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?

Option 1: $42 + 7\pi\ ext{cm}$

Option 2: $21\pi + 14\ ext{cm}$

Option 3: $42 + 14\pi\ ext{cm}$

Option 4: $7 + 14\pi\ ext{cm}$

Team Careers360 · Accepted Answer

Correct Answer: $42 + 14\pi\ ext{cm}$

Solution :
Given: The radius of the circles($r$) = 7 cm
Length of the string not in contact with circle = $2r+2r+2r= 6r = 42\ ext{cm}$
By symmetry, the angles swiped by a string on one circle = $120°$
Length of string touching the circle = $3 imes \frac{120^\circ}{360^\circ} imes 2 \pi r= 2\pi r=14\pi\ ext{cm}$
Total length of string = $42 + 14\pi\ ext{cm}$
Hence, the correct answer is $42 + 14\pi\ ext{cm}$.

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Question : Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?Option 1: 42+7π cmOption 2: 21π+14 cmOption 3: 42+14π cmOption 4: 7+14π cm

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Question : Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Option 1: $42 + 7 π cm$
Option 2: $21 π + 14 cm$
Option 3: $42 + 14 π cm$
Option 4: $7 + 14 π cm$