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Question 1174845: A 6 inch personal pizza has 590 calories, with 240 from fat. A 16 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 16 inch pizza. Hint... must use Area = Pi*r^2 proportions to solve this problem. Round the number to the nearest calorie
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a 6 inch personal pizza has a diameter of 6 which means it has a radius of 3 because radius = diameter / 2.
the area of the 6 inch pizza is equal to pi * r^2 = pi * 3^2 = pi * 9.
a 16 inch pizza has a diameter of 16 which means it has a radius of 8 because radius = diameter / 2.
the area of the 16 inch pizza is equal to pi * r^2 = pi * 8^2 = pi * 64.
if you divide the 16 inch pizza into 8 equal slices, then the area of each slice is equal to pi * 64 / 8 = pi * 8.
you have:
the area of the 6 inch pizza is pi * 9
the area of one slice of the 16 inch pizza is pi * 8.
the ratio of the area of the 6 inch pizza to the area of one slice of the 16 inch pizza is (pi * 9) / (pi * 8) which is equal to 9/8.
the ratio of the area of one slice of the 16 inch pizza to the area of the 6 inch pizza is (8 * pi) / (9 * pi) which is equal to 8/9.
since the number of calories in the 6 inch pizza is 590, then the number of calories in one slice of the 16 inch pizza is 8/9 * 590 = 524.44444.....
round to the nearest calorie and it becomes 524.
that's your solution.
the number of calories from fat in one slice of the 16 inch pizza was not asked for.
consequently, that information is extraneous to the problem and can be ignored.
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