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The length of an arc of a circle of radius 3.5 cm is  1...

The length of an arc of a circle of radius 3.5 cm is  1\(\frac{19}{36}\) cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take \(\pi = \frac{22}{7}\)] 

A.

55\(^o\)

B.

36\(^o\)

C.

25\(^o\)

D.

22\(^o\)

Correct answer is C

L = \(\frac{\theta}{360^o}\) = 2\(\pi\)

\(\frac{55}{36} = \frac{\theta}{360^o} \times 2 \times \frac{22}{7} \times 3.5\)

\(\theta = \frac{360 \times 55 \times 44 \times 0.5}{3 \times 44 \times 0.5}\)

= \(\theta = 25^o\)