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 $π =\frac{22}{7}$
Answer & explanation
Correct answer: option 3
Formula Used
Arc length of a circle , I = 2\(\Pi \)r x \(\theta \)/360
Calculation
Putting values in the formula, we get
= 19 = 2 x \(\frac{22}{7}\) x 30 x \(\theta \)/360
= \(\theta \)/360 = \(\frac{19 \;×\; 7}{44\;×\;30}\)
= \(\theta \) = \(\frac{133}{44\;×\;30}\) x 360 = \(\frac{133\;×\;12}{44}\) = \({36.27}^\circ\)
Therefore, the angle subtended at the center is \({36.27}^\circ\).