A pizza parlor in Tallahassee sells a pizza with a 16-inch diameter. A pizza parlor in Jaco, Costa Rica, sells a pizza with a 27.8-centimeter diameter.
Part A: How many square inches of pizza is the pizza from Tallahassee? Show every step of your work. (1 point)
Part B: How many square centimeters of pizza is the pizza from Jaco, Costa Rica? Show every step of your work. (1 point)
Part C: If 1 in. = 2.54 cm, which pizza has the larger area? Show every step of your work. (1 point)
Part D: Using the diameter of each pizza, determine the scale factor relationship between the pizzas. (1 point)
DO NOT MAKE LONG RESPONSES
Part A:
To find the area of the pizza from Tallahassee, we first need to calculate the radius: 16 inches / 2 = 8 inches.
Next, we use the formula for the area of a circle: A = πr^2, where π is approximately 3.14159.
A = 3.14159 * 8^2
A = 3.14159 * 64
A = 201.06176 square inches
Part B:
To find the area of the pizza from Jaco, Costa Rica, we first need to calculate the radius: 27.8 centimeters / 2 = 13.9 centimeters.
Next, we use the formula for the area of a circle: A = πr^2, where π is approximately 3.14159.
A = 3.14159 * 13.9^2
A = 3.14159 * 193.21
A = 606.158519 square centimeters
Part C:
To compare the two areas, we need to convert the area of the pizza from Tallahasse to square centimeters using the conversion factor 1 in = 2.54 cm.
201.06176 square inches * (2.54 cm / 1 inch)^2 = 1301.90948512 square centimeters
Comparing the two areas:
1301.90948512 square centimeters (Tallahassee) vs. 606.158519 square centimeters (Jaco, Costa Rica)
The pizza from Tallahassee has a larger area.
Part D:
Using the formula for the scale factor relationship between the pizzas:
Scale Factor = Diameter of Jaco, Costa Rica / Diameter of Tallahassee
Scale Factor = 27.8 cm / 16 in
Scale Factor = 1.7375