Question

An arc subtends a central angle measuring \dfrac{\pi}{2}

Answer 1

Arc Length is 1/4th of the circumference .

Step-by-step explanation:

Here we need to find fraction of the circumference is this arc when An arc subtends a central angle measuring $\dfrac{\pi}{2}$ radians ! Let's find out :

We know that circumference of an arc subtending a central angle of x is :

⇒ $Arc = \frac{Angle}{360}(2\pi r)$

⇒ $Arc = \dfrac{\frac{\pi}{2}}{360}(2\pi r)$

⇒ $Arc = \frac{90}{360}(2\pi r)$

⇒ $Arc = \frac{90}{90(4)}(2\pi r)$

⇒ $Arc = \frac{1}{4}(2\pi r)$

⇒ $Arc = \frac{1}{4}(Circumference)$

Therefore , Arc Length is 1/4th of the circumference .