Question : If the arc of a circle of radius 30 cm has a length of 19 cm, then the angle (in degrees, rounded off to two decimal places) subtended at the centre of the circle is:
(Take $\pi=\frac{22}{7}$)
Option 1: 51.25
Option 2: 16.27
Option 3: 36.27
Option 4: 46.25
Correct Answer: 36.27
Solution :
Given: Length of the arc of a circle = 19 cm
Radius = 30 cm
We know that,
Length of the arc = $\frac{\theta}{360^\circ}\times 2 \pi r$
⇒ $19= \frac{\theta}{360^\circ}\times 2 \times\frac{22}{7}\times 30$
⇒ $\theta=\frac{19\times7 }{2\times 22\times 30}\times 360^\circ$
⇒ $\theta=36.27^\circ$
Hence, the correct answer is 36.27.
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