Multiple choice

The circle in figure has center O, the length of minor $arc AB = 5\pi$ and m$\angle AOB = 50^{\circ}$. Calculate the area of the circle.

  1. $25\pi$
  2. $324\pi$
  3. $576\pi$
  4. $1,296\pi$
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B Correct answer
AI explanation

Using the arc length formula L = (theta/360) multiplied by 2*pi*r, we substitute 5*pi for L and 50 degrees for theta to get 5*pi = (50/360)2*pi*r. Solving this yields r = 18. The area of the circle is pi*r squared, so calculating pi(18 squared) gives 324*pi.

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