Question

for the circle of radius 9 feet, find the arc length s cut off by a central angle of 6 degrees.

Answer 1

Answer on Question #77227 – Math – Geometry

Question

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

Solution

Let $s$ represent the arc length, $\theta$ represent 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

$$s = r\theta.$$

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

$$180{}^{\circ} - \pi \text{ rad}$$ $$6{}^{\circ} - \theta \text{ rad}$$

Then

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

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

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

Answer: $s = \frac{3\pi}{10} \text{ ft}$

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