Krishna
0

Arc length:

Step 1: Note down the given values


Step 2: Set up the formula for arc length. 

NOTE: The formula is arc length= 2 \pi (r)(\frac{\theta }{360}) ,

where {\displaystyle r} equals the radius of the circle and {\displaystyle \theta } equals the measurement of the arc’s central angle, in degrees.

                        or 

Arc length = r * \theta


Step 3: Plug the length of the circle’s radius into the formula.


Step 4: Plug the value of the arc’s central angle into the formula. 


Step 5: Simplify the equation to find the arc length


NOTE: Use multiplication and division to simplify the equation.

  


Area of the circle.

Step 1: Identify the known or given information.


Step 2: Set up a formula for the sector area

            NOTE: A ratio will need to be constructed. Recall that a circle is composed

            of 360 degrees. Therefore, the following ratio can be made,

                         \frac{\theta}{360} = \frac{\text{sector area} (A_C)}{\text{Total area} (A_T)}

            Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

                where, \theta = Central angle.

Step 3: Plug the sector’s central angle measurement into the formula.  

Step 4: Plug the sector’s radius measurement into the formula.  

Step 5: Solve for the area:

            EXAMPLE: Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

                              Sector area = \frac{60}{360}*\left(3.14\right)\left(5\right)^2

                                  Sector area = 13.09 cm^2