Question

Little Italy Pizza charges 12.00 for a \(12^{\text {" diameter sausage }}\) pirza and \(\$ 14.00\) for a \(14^{\prime \prime}\) diameter sausage pizza. Write the pseudocode algorithm that calculates and displays how much each of these earns the establishment per square inch of pizza sold. (Hint: you will need to first calculate how many square inches there are in each pizza.)

Short answer

Answer: The price per square inch for the 12-inch pizza is $$\frac{1}{3\pi}$$ dollars, and the price per square inch for the 14-inch pizza is $$\frac{2}{7\pi}$$ dollars.

Step-by-step solution

Calculate the area of the pizzas

The formula to find the area (A) of a circle is given by A = πr^2, where r is the radius of the circle. Since the diameter is given, we can find the radius by dividing the diameter by 2. For the 12-inch pizza: Radius: \( 12^{\prime \prime} / 2 = 6^{\prime \prime}\) Area: $$A_1 = \pi (6^{\prime \prime})^2 = 36\pi \thinspace \text{square inches}$$ For the 14-inch pizza: Radius: \( 14^{\prime \prime} / 2 = 7^{\prime \prime}\) Area: $$A_2 = \pi (7^{\prime \prime})^2 = 49\pi \thinspace \text{square inches}$$

Calculate the price per square inch

Now that we have the area of both pizzas, we can calculate the price per square inch by dividing the total price of each pizza by its respective area. For the 12-inch pizza: Price per square inch: $$\frac{12.00}{36\pi} = \frac{1}{3\pi} \thinspace\text{dollars}$$ For the 14-inch pizza: Price per square inch: $$\frac{14.00}{49\pi} = \frac{2}{7\pi} \thinspace\text{dollars}$$

Display the result

The price per square inch for both pizzas is: 12-inch pizza: $$\frac{1}{3\pi} \thinspace\text{dollars per square inch}$$ 14-inch pizza: $$\frac{2}{7\pi} \thinspace\text{dollars per square inch}$$