Lois C. answered • 05/11/20
BA in secondary math ed with 20+ years of classroom experience
The formula for arc length ( the length of the outer edge of the crust) is given as s = r·θ where r is the radius and θ is the angle measure in radians. Since the diameter is 12, that makes the radius 6 inches. Since the pizza is cut into 8 equal slices, the central angle for each slice is 360/8 or 45º. When we convert this to radians by multiplying 45 by the conversion fraction of 180/π radians, we get π/4 radians as the angle measure. Now we multiply according to the formula: S = 6(π/4) = 3π/2 which is approximately equal to 4.71 inches.
Another way to solve this, or to check our answer once it is solved, is to take the entire circumference and divide it by 8 since there are 8 slices. Since C = πd, the circumference is ≈ 37.68 in, and dividing this by 8 gives us 4.71 inches, so either way we do it, we get the same answer.
