JAMB - Mathematics (2004 - No. 1)

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

60^o

120^o

180^o

30^o

Length of an arc = \(\frac{\theta}{360}\) x 2\(\pi\)r

22 = \(\frac{3x}{360}\) x \(\frac{22}{7}\) x 7 (since D = 2r)

22 x 7 x 360 = 3x X 22 X 7

x = \(\frac{22 \times 7 \times 360}{3 \times 22 \times 7\times 2}\) = 60º