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)

The radius of the pie is 6.17 in.

Step-by-step explanation:

The formula for arc length as a function of radius is

s = 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/Ф

and in this instance r = (7.85 in) / (π/4). Evaluating this, we get:

r = 6.17 in

The radius of the pie is 6.17 in.