Question

Find the arc length of a central angle of 7pi/3 in a circle whose radius is 3 inches.

A. 4pi/3 inches

B. 630 inches

C. 7pi/6 inches

D. 7pi inches

Answer 1

$\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \hrulefill\\ r=3\\ \theta =\frac{7\pi }{3} \end{cases}\implies s=3\cdot \cfrac{7\pi }{3}\implies s=7\pi$

Answer 2

Answer:

D. 7pi inches

Step-by-step explanation:

The value of the arc length is calculated by the following formula,

$s = rt$

Where:

1. s is the arc length
2. r is the radius of the circle
3. t is the central angle in radians

Since we were given both the central angle and the radius we can just plug it into the formula and solve for the arc length.

$s = \frac{7\pi }{3} *3$

$s = 7\pi$

Now we can see that the arc length has a value of $7\pi$ , making the answer of this question D. 7pi inches

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