Directions: 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 inches long, 14 1 inches wide, and 1 3 inches
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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 five sides.
Tony says he will make and sell your crazy pizza if you can prove the following:
• It is approximately the same area as the large pizza he sells now.
• It fits inside the large box listed above.
• It can be cut into 8‒12 equal-sized pieces.
Create one design for a crazy pizza that will meet all of Tony's requirements.
1. Create a representation of your design that includes measurements.
2. Prove mathematically, using appropriate formulas, that your design is approximately the same surface area as Tony’s large pizza.
3. Prove mathematically, using appropriate formulas, that your pizza will fit in the box.
4. Use diagrams or other models to prove that your design can be divided into 8‒12 equal-sized pieces. (Tip: You may use graph paper or the Virtual Geoboard to show how your pizza can be divided into equal-sized pieces.)
Your design and proofs (model and mathematical) will be submitted as your portfolio assessment.
why not just make it a regular octagon or dodecagon that has a width of 14" ?
You can easily determine that the area will be a bit bigger than that of a 14" diameter circle.
Can someone gicve me the answer
Give
Can a pentagon have a 14-inch diameter?
i would do the pentagon
To meet Tony's requirements, you need to design a crazy pizza shape that has approximately the same area as the large pizza he sells, fits inside the given rectangular box, and can be cut into 8-12 equal-sized pieces. Here's a step-by-step guide on how to accomplish each of these tasks:
1. Design a crazy pizza shape:
- Start by sketching a shape that has at least five sides. This shape can be any irregular polygon, so feel free to get creative.
- Label each side of the shape with its respective length.
2. Prove mathematically that your design has approximately the same surface area as Tony's large pizza:
- Calculate the area of your pizza shape using the appropriate formula for the type of shape you've designed. For irregular polygons, you can divide it into smaller, more regular polygons and calculate their areas individually. Add up the areas of all the smaller polygons to get the total area of your pizza shape.
- Use the formula for the area of a circle to calculate the area of Tony's large pizza. Remember that the diameter is given as 14 inches, so you can substitute it into the formula.
- Compare the two calculated areas to see if they are approximately equal. Keep in mind that there might be a slight difference due to the nature of the shapes.
3. Prove mathematically that your pizza will fit in the box:
- Calculate the volume of the given rectangular box using the formula for the volume of a rectangular prism. Substitute the given lengths into the formula to find the volume.
- Calculate the area of your pizza shape (found in step 2) by multiplying its length by its width.
- Compare the calculated area of your pizza shape to the volume of the box. If the area is smaller than or equal to the volume, then your pizza will fit inside the box.
4. Prove that your design can be divided into 8-12 equal-sized pieces:
- Use diagrams, graph paper, or Virtual Geoboard to demonstrate how your pizza can be divided into 8-12 equal-sized pieces.
- Divide your pizza shape into multiple smaller polygons of equal area and size without overlapping them. You can use lines or other structures to separate the pieces.
- Count the number of equal-sized pieces you've created. If it falls within the range of 8-12, then your design meets this requirement.
Remember to document your design, measurements, and calculations in your portfolio assessment as described. Good luck with your crazy pizza design!