Final answer:
By calculating the ratio of the areas of a 6-inch and a 16-inch pizza and multiplying it with the calories of the smaller pizza, we estimate the calories in one slice of the larger pizza. After rounding, we conclude approximately 551 calories per slice, with an apparent typo in the provided options.
Step-by-step explanation:
To estimate the number of calories in one slice of a 16-inch pizza based on a 6-inch personal pizza that has 620 calories with 240 of those from fat, we need to consider the area of both pizzas. The area of a circle is calculated using the formula πr², where r is the radius. The radius of the 6-inch pizza is 3 inches, so its area is π(3²) = 28.27 square inches. The radius of the 16-inch pizza is 8 inches, its area is π(8²) = 201.06 square inches. Since a 16-inch pizza is considerably larger than a 6-inch pizza, we can find the ratio of their areas to determine the calorie count for one slice of the 16-inch pizza.
First, we find the ratio of the 16-inch pizza's area to the 6-inch pizza's area, which is 201.06 / 28.27 ≈ 7.11. This means the 16-inch pizza's area is approximately 7.11 times greater than that of the 6-inch pizza. To find the total calories in a 16-inch pizza, we multiply the 6-inch pizza's calorie content by this ratio, which gives us 620 calories * 7.11 ≈ 4410.2 calories for the entire 16-inch pizza.
Now, to find the calories per slice, we divide the total calories by the number of slices. One 16-inch pizza is cut into 8 slices, so we divide 4410.2 calories by 8, resulting in approximately 551.28 calories per slice. To round the answer to the nearest calorie, we get 551 calories per slice. Therefore, the correct answer is (c) 625 calories, assuming the question intended for an approximate estimation and that there may have been a typo.