Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$
A) $s = \frac { 5 \pi } { 4 } \mathrm { ft }$

B) $s = 25 \pi \mathrm { ft }$

C) $s = \frac { 3 \pi } { 8 } \mathrm { ft }$

D) $s = \frac { 9 \pi } { 4 } \mathrm { ft }$

E) $s = 5 \mathrm { ft }$

Question

Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$
A) $s = \frac { 5 \pi } { 4 } \mathrm { ft }$

B) $s = 25 \pi \mathrm { ft }$

C) $s = \frac { 3 \pi } { 8 } \mathrm { ft }$

D) $s = \frac { 9 \pi } { 4 } \mathrm { ft }$

E) $s = 5 \mathrm { ft }$

Quizplus · Accepted Answer

The length of an arc of a circle is given by the formula $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. In this case, the radius is $3$ m and the central angle is $75 ^ { \circ }$, which is $\frac { 5 \pi } { 12 }$ radians. Therefore, the length of the arc is $s = 3 \cdot \frac { 5 \pi } { 12 } = \frac { 5 \pi } { 4 } \mathrm { m }$.

Find the Length of an Arc of a Circle of Radius