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An arc of a circle of length 22 cm subtends an angle of 3x\(^{\circ}\) at the ce...


Question

An arc of a circle of length 22 cm subtends an angle of 3x\(^{\circ}\) at the center of the circle. Find the value of x if the diameter of the circle is 14 cm

Options

A) 60\(^{\circ}\)

B) 120\(^{\circ}\)

C) 180\(^{\circ}\)

D) 30\(^{\circ}\)

The correct answer is A.

Explanation:

\( ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}\)

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Dicussion (1)

  • \( ARC\hspace{1mm}length = (\frac{\theta}{360})\times 2\pi r\\22=\frac{3x}{360}\times \left(2 \times(\frac{22}{7})\times(\frac{7}{1})\right)\\3x = 180\\x = \frac{180}{3}\\x = 60^{\circ}\)

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