Formulas for Arc Length - showmethemath.com

1 Formulas for Arc LengthIt helps to think of a pizza when working with these types of problems. The arc Length is the Length of the crust on the piece of pizza you get. If you get the whole pizza then the arc Length is the circumference of the pizza. If you get half the pizza then the arc Length is half the circumference of the each of the Formulas let C stand for circumference, rstand for radius, dstand for diameter, and lstand for arc Length . Use the formula C=2 rto calculate the circumference of a circle when the radius is given. Use the formula C= dto calculate the circumference of a circle when the diameter is can use C360 =lmeasureofthecentralangle ormeasureofthecentralangle360 =lCExample 1, finding the arc Length .

2 What is the Length of arc XY in circle A and B? What is the Length of arc XYZ in Circle D? Each circle has a radius of by writing the =lmeasureofthecentralangle Or measureofthecentralangle360 =lCSolving either of the Formulas for l you getl=measureofthecentralangle360 CFor circle A you get l=120 360 Cwhich simplifies to l=13 Cand since C=6 you end up with l=2 as the arc Length for arc circle B you get l=90 360 Cwhich simplifies to l=14 Cand since C=6 you end up with l=32 as the arc Length for arc circle D you get l=180 360 Cwhich simplifies to l=12 Cand since C=6 you end up with l=3 as the arc Length for arc 's Notes

3 Page 1 of 3 Formulas for Area of a SectorIt helps to think of a pizza when working with these type of problems. The area of the sector is the size of the piece of pizza you get. If you get the whole pizza then the area of the sector is the area of the pizza. If you get half the pizza then the area of the sector is half the area of the each of the Formulas let A stand for the area of the circle, rstand for radius, dstand for diameter, and Asecstand for the area of the sector. Use the formula d=2rto calculate the radius when the diameter is can use either of the Formulas below:areaofcircle360 =areaofsectormeasureofcentralangleormeas ureofcentralangle360 =areaofsectorareaofcircleExample 2, finding the area of a sector.

4 What is the area of sector XAY in circle A? What is the area of sector XBY in circle B? What is the area of sector XDZY in Circle D? Each circle has a radius of by writing the =Asecmeasureofthecentralangle Or measureofthecentralangle360 =AsecASolving either of the Formulas for Asec you getAsec=measureofthecentralangle360 AFor circle A you get Asec=120 360 Awhich simplifies to Asec=13 Aand since A=9 you end up with Asec=3 as the area for sector circle B you get Asec=90 360 Awhich simplifies to Asec=14 Aand since A=9 you end up with Asec=94 as the area for sector circle D you get Asec=180 360 Awhich simplifies to Asec=12 Aand since A=9 you end up with Asec=92 as the area

5 For sector 's Notes page 2 of 3 How Arc Length and Area of a Sector are Relatedarclengthcircumferenceofcircle=ar eaofsectorareaofcircleNate's Notes page 3 of 3