Question

In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π4 radians. What is the arc length? Use 3.14 for π . Enter your answer as a decimal in the box.

Answer 1

`\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=6\\ \theta =(7\pi )/(4) \end{cases}\implies s=6\cdot \cfrac{7\pi }{4}\implies s=\cfrac{21\pi }{2}`

Answer 2

`Arc length=32.97m`

Explanation:

It is given that In a circle with a radius of 6 m, an arc is intercepted by a central angle of
`(7\pi)/(4)` radians.

Then, the arclength of the circle is given as:

`Arc length=radius{*}central angle`

⇒
`Arc length=6{*}(7\pi)/(4)`

⇒
`Arc length=(21\pi)/(2)`

⇒
`Arc length=10.5{*}3.14`

⇒
`Arc length=32.97m`

Thus, the arc length of the given circle is 32.97m.