Question

If in a circle of radius r, an arc of length l subtends an angle Ɵ radian at the centre, then

Answer 1

Step-by-step explanation:

thita=arc/radius this the formula

Answer 2

Answer:

In a circle of radius $r$, an arc of length $l$ subtends an angle $\theta$ radians at the center, then the length $l$ is equal to $\frac{\pi r \theta}{180}$.

Step-by-step explanation:

Case1. When the arc subtends an angle of 360° at the centre.

Then, the arc is the circumference of the circle.

Thus, the length of the arc = The circumference of the circle

$l=2\pi r$

Case2. When the arc subtends an angle $\theta$ at the centre.

Then,

The length of the arc = $\frac{\theta}{360} \times 2\pi r$

                                   = $\frac{\pi r \theta}{180}$

Final answer: In a circle of radius $r$, an arc of length $l$ subtends an angle $\theta$ radians at the center, then the length $l$ is equal to $\frac{\pi r \theta}{180}$.

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