Mario Agnello is opening a new pizza shop in town. He plans to offer a 12-inch diameter pizza and an 18-inch diameter pizza. He has set the price of a 12-inch cheese pizza at 8.00$, based on the amount of ingredients needed to cover that size crust. If Mario would like to keep the pricing proportional, what should he charge for an 18-inch cheese pizza?

Question

anonymous · Answer

pls explain to me

whpalmer4 · Answer

Area of a pizza is given by $$A = \pi r^2$$If the 12 inch pizza costs $8, you can find the proportional cost for the 18 inch pizza by solving$$\frac{8}{\pi (12)^2} = \frac{x}{\pi (18)^2}$$where $x$ is the price of the 18 inch pizza.

whpalmer4 · Answer

oops, I've taken 12 and 18 as radii rather than diameters.  Because the mistake was made on both sides, it cancels out, but I'll rewrite it correctly:

$$\frac{8}{\pi (12/2)^2} = \frac{x}{\pi (18/2)^2}$$Cross-multiply and solve for $x$ to get the price of the 18 inch pizza.

nurali · Answer

Well in order to keep the pricing proportional, he needs to increase the price by the same ratio that the AREA of the pizza increases by.

So the ratio of the diameter of the 18 inch to 12 inch pizza is 18: 12 = 3: 2.

So the ratio of the areas is 3² : 2² = 9: 4

So the ratio of the prices should be 9: 4, and since the 12-inch pizza costs $8.00, that means th 18-inch pizza costs $18.00.

whpalmer4 · Answer

I do this computation or a variation nearly every time I go to a pizza joint :-)