Name: Date: Period: PIZZA! PIZZA! Area of Circles and Squares Circumference and Perimeters Volume of Cylinders and Rectangular Prisms Comparing Cost Lesson One Day One: Area and Cost A. Area of Pizza Triplets Jim, Joe, and Jeff want to order pizza for their upcoming triple birthday party. Since their money is limited, they decide to compare costs of pizzas to make sure they get the best value for their money. The brothers want a variety of pizzas and think having both round and square pizzas would be a good idea. So they first decide to compare sizes and surface areas of pizzas. Joe thinks he and his brothers need to get organized in their comparisons by making a table of their findings. So Joe creates tables that include sizes, shapes, and areas of common pizzas sold at their favorite restaurants along with price comparisons for supreme pizzas. On the next page, calculate the area of each size pizza. Round the areas to the nearest whole square inch. On your handout titled, PIZZA SIZE AND PRICE COMPARISONS, record your data in column 2, Area of Pizza. The following formulas may be helpful: Area of a circle = π r 2 Use 3.14 as the value of π if not using a scientific calculator. Area of a square = length x width Pizza! Pizza! Student Materials Page 1 of 12
Personal Pan Pizzas 6 inches 6 inches Small Pizzas 9 inches 9 inches Medium Pizzas 12 inches 12 inches Large Pizzas 15 inches 15 inches Pizza! Pizza! Student Materials Page 2 of 12
B. Interpreting Data Jim, Joe, and Jeff are surprised when they find out the areas and prices of the pizzas at their two favorite pizza restaurants. One restaurant specializes in the square pizzas listed on your handout, while the other restaurant bakes round pizzas. Write three observations they make regarding sizes, shapes, and/or prices of pizzas from the data on your handout. Observation 1: Observation 2: Observation 3: Pizza! Pizza! Student Materials Page 3 of 12
Comparisons Jeff, the oldest of the triplets, notices some relationships in the areas of a few of the pizzas. He thinks this will help the brothers decide which pizzas will be the best value. First, Jeff sees that two 12-inch round pizzas are about equal in area to one 15-inch square pizza. How do they compare in cost? Next, Jeff notices that the area of a 6-inch square personal pan pizza goes into the area of a 12-inch square pizza an exact number of times. How many 6-inch square pizzas equal one 12-inch square pizza? How much would you pay for the 6-inch pizzas? Which is the better value if you compare the equivalent areas? Finally, Jeff gets carried away with his mental math expertise and notices that if he buys four 12-inch square pizzas he will have the same amount of pizza as a certain number of 9-inch round pizzas. He decides to let his brothers have a little mental exercise and figure out how many 9-inch round pizzas equal four 12-inch square pizzas. What do they get for an answer? Cost of the 12-inch square pizzas? Cost of the 9-inch round pizzas? How do the prices compare? Pizza! Pizza! Student Materials Page 4 of 12
F. $80.00 Budget The brothers now must decide how much pizza they can buy on their budget of $80.00. Since they are triplets born on the third day of the third month, they decide to get three slices of pizza for each guest. They plan to feed 15 guests plus themselves at the birthday party. How many slices of pizza do they need to purchase? Since Jim, Joe, and Jeff want to have both round and square pizzas, find three combinations of pizzas within their $80.00 budget that could give them enough pizza for the party with only a few or no slices left over. You may or may not need all the rows on the tables. Order Combination 1 # of Pizzas Total # of Slices Size, Shape, and Cost per Pizza Total Cost per Size Total Slices: Total Cost: Order Combination 2 # of Pizzas Total # of Slices Size, Shape, and Cost per Pizza Total Cost per Size Total Slices: Total Cost: Pizza! Pizza! Student Materials Page 5 of 12
Order Combination 3 # of Pizzas Total # of Slices Size, Shape, and Cost per Pizza Total Cost per Size Total Slices: Total Cost: G. Calculating Area of Pizza Orders and Cost per Square Inch Calculate the area of pizza purchased by each order and the cost per square inch of pizza for each order. Show your work. Order Combination 1 Order Combination 2 Order Combination 3 Which order is the best value? Pizza! Pizza! Student Materials Page 6 of 12
Lesson Two: Volume A. The local pizza restaurants sell frozen pizzas to supermarkets throughout Washington. To ship the frozen pizzas, the pizzas are packed twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical and rectangular shipping cartons for the different size pizzas? Volume of a Rectangular Prism = length x width x height or Volume = (area of square pizza) x (height of carton) Volume of a Right Cylinder = π r 2 h or Volume = (area of round pizza) x (height of the carton) Volume of Shipping Cartons for 12 Frozen Pizzas Square Pizzas Volume of Carton Round Pizzas Volume of Cylinder 6-inch square 9-inch square 12-inch square 15-inch square 6-inch round 9-inch round 12-inch round 15-inch round Show work on the next page and record the data above. Pizza! Pizza! Student Materials Page 7 of 12
Pizza! Pizza! Student Materials Page 8 of 12
Computing Volumes for Pizza Cartons 12 Pizzas per Carton Hint: Height of all cartons will be 12 inches. 6-inch square 6-inch round 9-inch square 9-inch round 12-inch square 12-inch round 15-inch square 15-inch round B. Compare the volume of a shipping carton for four 6-inch square personal pan pizzas with the carton for one 12-inch square pizza. The amount of pizza is the same for both and all the pizzas are one inch thick. Show your work here. Volume for four 6-inch square pizzas? Volume for one 12-inch square pizza? How do the prices compare for the two orders? (Refer back to handout.) Pizza! Pizza! Student Materials Page 9 of 12
Lesson Three: Circumference and Perimeter Jeff was surprised when he noticed that the area of the square and round pizzas with the same width and diameter were so different. He wondered if there would be a relationship between the perimeter of the square pizzas and the circumference of the round pizzas. Find the circumference of the round pizzas and the perimeter of the square pizzas. Show your work in the boxes. Perimeter of a Square = Side + Side + Side + Side or Perimeter of a Square = 4S Circumference of a Circle = 2π r or Circumference of a Circle = dπ 6-inch square 6-inch round 9-inch square 9-inch round 12-inch square 12-inch round 15-inch square 15-inch round Which two pizzas measure about the same around the outside edge? Looking back on the handout, how do their areas compare? Pizza! Pizza! Student Materials Page 10 of 12
A 6-inch square pizza is half the perimeter of a 12-inch square pizza, but their areas are quite different. Compare the areas of two 6-inch square pizzas to one 12-inch square pizza. The circumference of five 6-inch round pizzas is about the same length as two perimeters of which size pizza? What is the area of five 6-inch round pizzas? What is the difference between the areas of these pizzas? Pizza! Pizza! Student Materials Page 11 of 12
Name: Date: Period: PIZZA SIZE AND PRICE COMPARISONS Personal Pan Pizzas (4 slices per pizza) Size & Shape Area of Pizza Price of Pizza 9-inch round $8.99 9-inch square $7.99 Small Pizzas (6 slices per pizza) Size & Shape Area of Pizza Price of Pizza 9-inch round $11.99 9-inch square $9.99 Medium Pizzas (8 slices per pizza) Size & Shape Area of Pizza Price of Pizza 12-inch round $13.99 12-inch square $11.99 Large Pizzas (12 slices per pizza) Size & Shape Area of Pizza Price of Pizza 15-inch round $15.99 15-inch square $14.99 Pizza! Pizza! Student Materials Page 12 of 12