SOLUTION: 'ET Pizza' produces two pizzas that are similar in shape. The smaller pizza is 20 cm in diameter and costs $10. The larger pizza is 30 cm in diameter. What is a fair cost for the l

Algebra ->  Proportions  -> Lessons -> SOLUTION: 'ET Pizza' produces two pizzas that are similar in shape. The smaller pizza is 20 cm in diameter and costs $10. The larger pizza is 30 cm in diameter. What is a fair cost for the l      Log On


   

Question 1054046: 'ET Pizza' produces two pizzas that are similar in shape. The smaller pizza is 20 cm in diameter and costs $10. The larger pizza is 30 cm in diameter. What is a fair cost for the larger pizza?
Thanks in advance.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
radius is equal to 1/2 * diameter.

radius of the smaller pie is 10 cm.

radius of the larger pie is 15 cm.

the area of the smaller pizza is equal to pi * r^2 which is equal to pi * 10^2 = 100 * pi.

the area of the larger pizza is equal to pi * r^2 which is equal to pi * 15^2 = 225 * pi.

the ratio of the larger area to the smaller are is (225 * pi) / (100 * pi) which is equal to 2.25.

2.25 * 10 = 22.5

that appears to be a fair price for the large pie since it consumes about 2.25 times the ingredients as in the smaller pie.