Question

Given the radius, in inches, and price of a pizza, design an algorithm to find the price of the pizza per square inch.

Short answer

Divide the pizza price by its area calculated using \( A = \pi r^2 \).

Step-by-step solution

Understand the Formula for Area

To find the price per square inch, we first need to figure out the area of the pizza. The area of a circle (pizza) is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the pizza.

Calculate the Area of the Pizza

Substitute the given radius of the pizza into the formula \( A = \pi r^2 \). This will give us the area in square inches.

Use the Price-to-Area Formula

With the area calculated, we can find the price per square inch using the formula: \( \text{Price per square inch} = \frac{\text{Price of pizza}}{\text{Area of pizza}} \).

Substitute and Solve

Substitute the area calculated in Step 2 and the given price of the pizza into the formula from Step 3 to get the price per square inch. Ensure units are consistent, which should all be in inches and price currency.

Key concepts

Problem Solving

When tasked with finding the price per square inch of a pizza, it's essential to break the problem into manageable parts. Problem-solving often involves identifying knowns and unknowns, then forming a strategy around connecting them. In this scenario, we start by understanding the formula for the area of a circle, because a pizza's shape is circular. Once we know the area, we can then determine how to calculate the desired metric, which is the cost per unit area.

Here's a simple process for approaching such challenges:

• Identify the core components of the problem – in this case, radius, area, and price.
• Formulate a mathematical approach by using relevant formulas like the area of a circle.
• Calculate and analyze each step carefully to ensure accuracy in the final solution.

This approach to problem-solving is essential in mathematics and programming as it helps to unravel complex tasks into simple, easy-to-solve steps.

Mathematics in Programming

Mathematics plays a crucial role in programming, particularly when it comes to applying formulas to solve real-life problems. In the example of calculating the price per square inch of a pizza, we incorporate mathematical formulas directly into our algorithm. The area formula for a circle, \( A = \pi r^2 \), is pivotal in determining the total number of square inches.

Once the area is calculated, the formula for price per unit area is applied, \( \text{Price per square inch} = \frac{\text{Price of pizza}}{\text{Area of pizza}} \). Notice how traditional mathematical concepts translate directly to programming logic. This requires programmers to have a good understanding of mathematics so they can utilize these formulas correctly. The importance lies in:

• Translating mathematical equations into code efficiently.
• Ensuring precision in operations due to the inherent nature of mathematical calculations.
• Applying basic algebra and geometry together with logic to solve given problems.

Understanding these concepts is vital for any programmer, as math often underpins the logic of the algorithm being developed.

Geometry in Programming

When dealing with real-world shapes in programming, like a pizza in this case, geometry comes into play. Understanding the geometric properties of shapes allows programmers to manipulate and analyze them efficiently. The pizza problem is a classic example of applying geometric principles to solve practical tasks.

The first step involves recognizing the shape of the pizza as a circle, prompting the use of the circle area formula, \( A = \pi r^2 \). Geometry helps in:

• Calculating dimensions and areas accurately from given geometric shapes.
• Utilizing geometric transformations to perform real-time calculations.
• Applying properties of shapes to develop simulations and visual graphics.

Incorporating geometry in programming opens up a wide range of possibilities, from simple area calculations to more complex applications like game development and computer graphics. The precise use of geometrical formulas and concepts ensures that programs accurately reflect the desired outcomes in real-world scenarios.