Answer:
A: the pizza from Portland has an area of approximately 254.47 square inches
B: the pizza from San Anita, Peru, has an area of approximately 114.13 square inches.
C: the pizza from Portland has a larger area.
D: the pizza from San Anita, Peru, is about 0.67 times the size of the pizza from Portland.
Explanation:
Part A: To find the area of the pizza from Portland, we need to use the formula for the area of a circle, which is A = πr^2. First, we need to find the radius of the pizza. The diameter is given as 18 inches, so the radius is half of that, which is 9 inches. Next, we can plug the radius into the formula and calculate the area: A = π(9 inches)^2 A = π(81 square inches) A ≈ 254.47 square inches So, the pizza from Portland has an area of approximately 254.47 square inches. Part B: To find the area of the pizza from San Anita, Peru, we can use the same formula, but we need to convert the diameter from centimeters to inches. The diameter is given as 30.6 centimeters. Using the conversion factor 1 inch = 2.54 centimeters, we can convert the diameter to inches: 30.6 centimeters ÷ 2.54 centimeters/inch ≈ 12.05 inches Now that we have the diameter in inches, we can find the radius by dividing it by 2: 12.05 inches ÷ 2 ≈ 6.03 inches Plugging the radius into the formula, we can calculate the area: A = π(6.03 inches)^2 A = π(36.36 square inches) A ≈ 114.13 square inches So, the pizza from San Anita, Peru, has an area of approximately 114.13 square inches. Part C: To compare the areas of the two pizzas, we need to convert the area of the pizza from Portland to square centimeters. Using the conversion factor 1 inch = 2.54 centimeters, we can convert the area: 254.47 square inches × (2.54 centimeters/inch)^2 ≈ 1639.70 square centimeters Comparing this to the area of the pizza from San Anita, Peru (which is 114.13 square inches), we can see that the pizza from Portland has a larger area. Part D: The scale factor relationship between the pizzas can be determined by comparing their diameters. The diameter of the pizza from Portland is 18 inches, and the diameter of the pizza from San Anita, Peru, is 30.6 centimeters. To compare these two values, we need to convert the diameter of the pizza from Portland to centimeters: 18 inches × 2.54 centimeters/inch ≈ 45.72 centimeters Now, we can calculate the scale factor: Scale factor = Diameter of pizza from San Anita, Peru ÷ Diameter of pizza from Portland Scale factor = 30.6 centimeters ÷ 45.72 centimeters Scale factor ≈ 0.67 So, the scale factor relationship between the pizzas is approximately 0.67, which means that the pizza from San Anita, Peru, is about 0.67 times the size of the pizza from Portland.
Hope this helped!