An arc of a circle of length 22 cm subtends an angle of 3x° at the center of the circle. Find the value of x if the diameter of the circle is 14 cm
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Correct Answer: Option A
Explanation:
\( ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}\)
\( ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}\)