Crazy Pizza Portfolio. Math 6B: Geometry and measurement.
A large pizza at Tony’s pizzeria is a circle with a 14-inch diameter. Its box is a rectangular prism that is 14 1/8 inches long, 14 1/8 inches wide, and 1 3/4 inches tall. Your job is to design a crazy new shape for a large pizza. It can be any irregular polygon shape, but it must have at least 5 sides.
What’s that answer?
Bro… Really!
just make some cuts so that you end up with five or more sides, with no circular arcs between them. You know it will fit the box, since the original circle did.
To design a crazy shape for the large pizza, we need to create an irregular polygon shape with at least 5 sides. Let's start by understanding the given dimensions and using them to create a new shape.
The diameter of the original pizza is 14 inches. This means the radius (half of the diameter) is 7 inches.
Since we want a polygon shape, we can start by drawing a regular polygon with 5 sides (a pentagon) that fits within the given diameter. To do this, we need to calculate the side length of the pentagon.
To find the side length of the regular pentagon, we divide the circumference of the circle (which is equal to the perimeter of the pentagon) by 5:
Circumference of the circle = π × diameter
Circumference of the circle = 3.14 × 14 inches
Circumference of the circle ≈ 43.96 inches
Perimeter of the pentagon = 5 × side length
Therefore, the side length of the pentagon is:
Side length = Perimeter of the pentagon / 5
Side length ≈ 43.96 inches / 5
Side length ≈ 8.79 inches
Now that we have the side length, we can use it to draw a regular pentagon with a side length of 8.79 inches.
To incorporate the given dimensions of the pizza box, we can use the length and width of the box as the dimensions for our new shape. The height of the box does not have a direct influence on the shape of the pizza, so we don't need to consider it in this case.
Therefore, our new crazy shape for the large pizza is a regular pentagon (5 sides) with a side length of approximately 8.79 inches, and its dimensions will be 14 1/8 inches long and 14 1/8 inches wide.
Please note that the shape's area, perimeter, and other properties may vary based on how the pentagon is positioned within the rectangle.
To design a crazy new shape for a large pizza, you are asked to create an irregular polygon shape with at least 5 sides. Here's how you can proceed:
Step 1: Understand the given information
Start by understanding the dimensions of the pizza and its box.
The large pizza at Tony's pizzeria has a 14-inch diameter. This means it is a circle with a radius of 7 inches. You can use this information to determine the area and circumference of the pizza.
The box of the pizza is a rectangular prism with dimensions 14 1/8 inches long, 14 1/8 inches wide, and 1 3/4 inches tall. You can use this information to determine the volume of the box.
Step 2: Sketch the irregular polygon shape
Visualize the different irregular polygon shapes that can fulfill the given requirements. For example, you can consider shapes like a pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), and so on. Sketch these shapes on a piece of paper or using a geometry software if available.
Step 3: Calculate the area of the irregular polygon shape
Once you have sketched your preferred irregular polygon shape, you need to calculate its area. The method for calculating the area of irregular polygons varies depending on their shape. For many irregular polygons, you can split them into simpler shapes (triangles, rectangles) and calculate their area individually. You may need to use trigonometry, side lengths, and angles to calculate the areas accurately.
Step 4: Compare the area with the pizza's area
Compare the calculated area of your irregular polygon shape with the area of the large pizza. You can find the area of the pizza by using the formula: Area = π * r^2, where r is the radius of the circle (7 inches).
If your irregular polygon shape's area is greater than or equal to the pizza's area, then it can accommodate the pizza without any overflow. If the area is less than the pizza's area, you may need to adjust the dimensions of your shape to ensure it can hold the pizza.
Step 5: Optional - Calculate the volume of the irregular box
If you wish to be creative and design an irregular box for your pizza, you can use the same approach as step 3 to calculate the volume. Measure the dimensions of your irregular box, split it into simpler shapes if necessary, and calculate the volume using the appropriate formulas.
By following these steps, you can design a crazy new shape for a large pizza that fulfills the given requirements.