Question

If a pizza with a diameter of 12 inches costs $10.99, based on area, about how much should a 15-inch pizza cost?

Answer 1

I'll show you two ways you could approach this problem (first method is easier to understand, second one is faster but requires a bit of higher-level thinking)

area of a circle = pi * r^2

divide the diameters by 2 to find the radii

then calculate the surface area of both pizzas and set up a proportion:

(area of large pizza) / (area of small pizza) = (cost of large) / (cost of small

and solve for the cost of the large (15 inch) pizza

Answer 2

now, for the second method, you could recall that surface area is proportional to the square of the radii. actually, it's also proportional to the square of the diameters as well.

a = pi*r^2
re-writing r in terms of d
a = pi*(1/2 * d)^2 = (1/4) * pi * d^2

therefore, the large pizza is (15/12)^2 times the small pizza, and therefore should cost (15/12)^2 as much

don't stress if you don't understand this one, the first method works just fine