A pecan pie is being served for dessert. One piece of pie has an arc length of 7.85 in. It has been cut into 8 equal pieces. What is the radius of the pecan pie? (Round to the nearest whole number)

Answer:The radius of the pie is 6.17 in.Step-by-step explanation:The formula for arc length as a function of radius iss = r·Ф, where Ф is the central angle in radians.Here we know that the arc length is 7.85 in.  Assuming that the whole pie has been cut into 8 equal pieces, the central angle of one such piece is 2π / 8, or π /4 (radians).thus, s = r·Ф, solved for r, is r = s/Фand in this instance r = (7.85 in)/(π/4).  Evaluating this, we get:                                  r = 6.17 inThe radius of the pie is 6.17 in.