In this practice, you will divide a circle into different sectors and verify arc length for each sector. Remember: An arc is a fraction of a circle.
First: Draw a four inch diameter circle.
Second: Draw in a diameter.
Third: Draw a line perpendicular to the diameter using the center of the circle as a point on the perpendicular line. Extend this line to also make it a diameter.
These actions divide the circle into four quadrants. (A quadrant is one fourth of a circle, a 90° sector.)
Fourth: Number the quadrants as shown. In quadrant 1, bisect the right angle to create two 45° arcs.
Fifth: In quadrant 2, use the radius of the circle as the compass setting and mark a 60° arc. Draw a line from the center of the circle to the mark on the circle.
Sixth: Calculate the length of the opposite side of a right triangle which has a 40° reference angle and an adjacent side of 2" (length of
the radius). In the third quadrant, use the line between quadrant 3 and 4 as the
adjacent side of a triangle and draw in the opposite side using the measurement from the above calculation. Next, draw in the hypotenuse of the right triangle. This drawing shows the different angles drawn in.
Seventh: Cut the circle out. The circumference of the circle is found by using the formula ¼ d. Roll out the circle to confirm that it is 12.5663" or 12 9/16".
Eighth: Now cut the circle into parts, using the lines you have drawn in as cutting guides.
You have seven sectors: one 90° , two 45° , one 30° , one 45° , one 50° , and one 60° .
With these seven sectors you can confirm your calculations for arc length.
Ninth: Calculate arc length for each arc and confirm your calculations by rolling out and measuring each of the arcs.