Question : An arc on a circle, whose length is 19.25 cm, subtends an 18° angle at the centre. What is the area of the circle? [Use $\pi = \frac{22}{7}$]
Option 1: 11796.625 cm2
Option 2: 11786.625 cm2
Option 3: 11780.625 cm2
Option 4: 11790.625 cm2
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Correct Answer: 11790.625 cm 2
Solution :
Here, $2 × \pi × r × \frac{\theta }{360°} = 19.25$
Where $r$ is the radius and $\theta$ is the central angle of the arc.
⇒ $2 × \frac{22}{7} × r × \frac{18 }{360} = 19.25$
⇒ $r = \frac{35 × 7}{4} = \frac{245}{4}$
Now, area of the circle is $\pi {r^2} = \frac{22}{7} × \frac{245}{4} × \frac{245}{4} = 11790.625$ cm
2
Hence, the correct answer is 11790.625
cm
2
.
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