The arc length of a circle is the distance around an arc.
It can be calculated using the formula above:
[tex]S=\frac{a}{360}\cdot2\cdot\Pi\cdot r[/tex]
Where:
S is the arc length;
a is the central angle, in degrees;
r is the radius.
To solve this problem, you can follow the steps.
Step 1: Extract the information from the exercise.
To solve the question, it is necessary to know "a" and "r".
From the question,
a = 70 °
r = 50 cm
Step 2: Substitute the values in the equation.
[tex]\begin{gathered} S=\frac{a}{360}\cdot2\cdot\Pi\cdot r \\ S=\frac{70}{360}\cdot2\cdot\Pi\cdot50 \end{gathered}[/tex]
Step 3: Solve the equation.
[tex]\begin{gathered} S=\frac{7000}{360}\pi \\ S=19.444\pi \end{gathered}[/tex]
S = 19.44π cm.
Step 4: To find the approximate solution, substitute π by 3.14.
[tex]\begin{gathered} S=19.444\cdot3.14 \\ S=61.1\operatorname{cm} \end{gathered}[/tex]
S = 61.1 cm.
Answer: The arc length is 19.44π cm or 61.1 cm.
