Question

For a circle of radius 9 feet, find the arc length s cut off by a central angle of 6°

Answer 1

$\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=9\\ \theta =6 \end{cases}\implies s=\cfrac{\pi (6)(9)}{180}\implies s=\cfrac{3\pi }{10}\implies s\approx 0.94$

Answer 2

The arc length s cut off by a central angle of 6 degrees

$s=\frac{3 \pi}{10} f t$.

How to estimate arc length?

Let 's' define the arc length, '$\theta$' define the central angle in radians and 'r' be the radius of the circle. Then a central angle of '$\theta$' radians in a circle of radius r subtends an arc of length.

We must define $6^{\circ}$ in radians

$s=r \theta$

$180^{\circ}-\pi \mathrm{rad}$

$6^{\circ}-\theta \mathrm{rad}$

Then

$\theta=\frac{6}{180} \cdot \pi=\frac{\pi}{30}$

The arc length s cut off by a central angle of 6 degrees

$s=9 f t\left(\frac{\pi}{30}\right)=\frac{3 \pi}{10} \mathrm{ft}$

$s=\frac{3 \pi}{10} f t$.

Therefore, the arc length s cut off by a central angle of 6 degrees is

$s=\frac{3 \pi}{10} f t$.

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