Question

Calculate the arc length S and area A of the following sector.a =70°r= 50 cmRound to the nearest whole number as needed

Answer 1

The arc length of a circle is the distance around an arc.

It can be calculated using the formula above:

`S=(a)/(360)\cdot2\cdot\Pi\cdot r`

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.

`\begin{gathered} S=(a)/(360)\cdot2\cdot\Pi\cdot r \\ S=(70)/(360)\cdot2\cdot\Pi\cdot50 \end{gathered}`

Step 3: Solve the equation.

`\begin{gathered} S=(7000)/(360)\pi \\ S=19.444\pi \end{gathered}`

S = 19.44π cm.

Step 4: To find the approximate solution, substitute π by 3.14.

S = 61.1 cm.

Answer: The arc length is 19.44π cm or 61.1 cm.