Multiple choice

In a circle a central angle of $60^o$ intercepts an arc of 15 inches. How many inches is the radius of the circle?

  1. $\dfrac{45}{\pi}$
  2. $\dfrac{\pi}{5}$

  3. 4
  4. $\dfrac{2\pi}{3}$

  5. not computable from given data
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A Correct answer
Explanation

Arc length s = r * theta (where theta is in radians). 60 degrees = pi/3 radians. 15 = r * (pi/3). r = 15 * 3 / pi = 45/pi.

AI explanation

The relationship between arc length, radius, and the central angle in radians is given by the formula arc length equals radius times the angle. A central angle of 60 degrees converts to radians by multiplying 60 by pi divided by 180, yielding pi divided by 3. Setting 15 equal to the radius times pi divided by 3, we solve for the radius to get 45 divided by pi.

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