Multiple choice

If a piece of wire 20 cm long is bent into an arc of a circle subtending an angle of ${ 60 }^{ \circ }$ at the center, then the radius of the circle (in cms) is:

  1. $\dfrac { \pi }{ 120 } $
  2. $\dfrac { \pi }{ 60 } $
  3. $\dfrac { 120 }{ \pi } $
  4. $\dfrac { 60 }{ \pi } $
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D Correct answer
Explanation

Arc length L = (theta/360) * 2 * pi * r. 20 = (60/360) * 2 * pi * r. 20 = (1/6) * 2 * pi * r. 20 = (1/3) * pi * r. r = 60/pi.

AI explanation

The length of an arc is calculated using the formula l = r * theta, where the angle theta must be in radians. First, convert the given angle of 60 degrees to radians by multiplying by pi/180, which gives theta = pi/3. Equating the wire length to the arc length gives 20 = r * (pi/3). Solving this equation for r yields r = 60/pi.

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