Question

example 3: comparing pizzas (1 of 2)
a pizzeria sells a rectangular 18 in. by 24 in. pizza for the same price as its large round pizza (24 - in. diameter). if both pizzas are of the same thickness, which option gives the most pizza for the money?
solution
we need to compare the areas of the pizzas. fortunately, geometry has provided algebraic models that allow us to compute the areas from the given information.

Explanation:

Step1: Calculate area of rectangular pizza

The area formula for a rectangle is $A = l\times w$. Here, $l = 24$ in and $w = 18$ in. So, $A_{rectangle}=24\times18 = 432$ square - inches.

Step2: Calculate area of round pizza

The area formula for a circle is $A=\pi r^{2}$, where the diameter $d = 24$ in, so the radius $r=\frac{d}{2}=12$ in. Then $A_{circle}=\pi\times(12)^{2}=144\pi\approx144\times3.14 = 452.16$ square - inches.

Step3: Compare the areas

Since $452.16>432$, the round pizza has a larger area.

Answer:

The large round pizza gives the most pizza for the money.