Solve the problem.
-On a circle of radius 12 meters, how long is an arc that subtends a central angle of $140 ^ { \circ }$ ?
A) $\frac { 28 \pi } { 3 } \mathrm {~m}$
B) $1680 \pi \mathrm { m }$
C) $\frac { 28 } { 3 } \mathrm {~m}$
D) $1680 \mathrm {~m}$

Question

Quizplus · Accepted Answer

To find the length of an arc, we use the formula $s = r	heta$, where $s$ is the length of the arc, $r$ is the radius of the circle, and $	heta$ is the central angle in radians.

First, we need to convert the central angle from degrees to radians. We know that $360^\circ$ is equivalent to $2\pi$ radians, so we can set up a proportion:

$$\frac{140^\circ}{360^\circ} = \frac{	heta}{2\pi}$$

Simplifying, we get:

$$	heta = \frac{7\pi}{18}$$

Now we can plug this into the formula for arc length:

$$s = 12\left(\frac{7\pi}{18}ight) = \frac{28\pi}{3} \mathrm{m}$$

Therefore, the answer is choice A, $\frac{28\pi}{3} \mathrm{m}$.

Solve the Problem 140∘140 ^ { \circ }140∘ ? A) 28π3 m\frac { 28 \pi } { 3 } \mathrm {~m}328π​ m

Solve the Problem $140 ^ { \circ }$ ?
A) $\frac { 28 \pi } { 3 } \mathrm {~m}$