Question : If the radius of the circle is 42 cm and the angle formed at the centre by an arc is 150°. What is the length of the corresponding area?
Option 1: 66 cm
Option 2: 77 cm
Option 3: 110 cm
Option 4: 55 cm
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Correct Answer: 110 cm
Solution :
The angle formed by the arc at the centre = 150°
The radius of the circle ($r$) = 42 cm
Length of the arc (l) = $2\pi r \times (\frac{\theta}{360°}$)
Where,
$\theta$ = Angle formed at the centre
$r$ = Radius of circle
Let the angle formed at the centre be $\theta$.
l = $2\pi r \times (\frac{θ}{360}$)
⇒ l = $2\pi \times 42 \times (\frac{150}{360}$)
⇒ l = $2 \times (\frac{22}{7}) \times 42 \times (\frac{5}{12})$
$\therefore$ l = $110$ cm
Hence, the correct answer is 110 cm.
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