Final answer:
To calculate the length of icing around each slice, find the circular arc length of one slice given the 8-slice division of the circumference, which is 3.9 inches when rounded to the nearest tenth, then multiply by 8 to get the total for all slices, which is closest to 9.4 inches.
Step-by-step explanation:
The question asks to calculate the length of icing needed around each slice of a birthday cake with a radius of 5 inches, assuming there are 8 slices in the cake. To find this, we need to determine the circular arc length of one slice. Since the full circumference of the cake is C = 2 π r, where r is the radius, we first calculate the total circumference of the cake using the given radius (5 inches) to be C = 2 π (5 in) = 10π in. As there are 8 slices, each slice will have an arc that is ⅘ of the total circumference. Therefore, the arc length for each slice is ⅘ × 10π in = ⅘ × 31.4159 in ≈ 3.92699 in. When rounded to the nearest tenth, this is approximately 3.9 inches. The correct answer choice that is closest to our calculation and given in the options is B) 9.4 in, as we need to multiply the arc length by 8 to get the total icing needed for all slices.