Chapter 2.8, Problem 15P

Writing A pizza shop sells small 6 in. pizzas and medium 12 in. pizzas. Should the medium pizzas cost twice as much as the small pizzas because they are twice the size? Explain.

To determine

To Find: The price of the larger pizza.

Answer to Problem 15P

No

Explanation of Solution

Given:

Diameter of smaller pizza, $d=6\text{in}$

Diameter of medium pizza, $D=12\text{in}$

Formula used:

Area of circle

  $A=\pi r^2$

Where,

R is the radius of that circle

Calculation:

Area of medium circle,

  $\begin{array}{l}A=\pi R^2\\ A=\pi \frac{D^2}{4}\\ A=\pi \frac{{\left(12\right)}^2}{4}\\ A=36\pi \mathrm{...}\left(1\right)\end{array}$

Area of smaller circle,

  $\begin{array}{l}a=\pi r^2\\ a=\pi \frac{r^2}{4}\\ a=\pi \frac{{\left(6\right)}^2}{4}\\ a=8\pi \mathrm{...}\left(2\right)\end{array}$

From equation (1) and (2)

  $A=4a$

Since the area of the medium circle is 4 times the area of the smaller circle

Therefore, the cost of the medium pizza should also equal the four times the cost of the medium pizza.

Conclusion:

No, the cost of medium pizza should not cost twice as much as small pizza instead it should cost four times the cost of small pizza.