Final answer:
To find out the cost of a 16" pizza, given that a 12" pizza costs $10.80, calculate the area of both pizzas and determine cost per square inch using the area of the 12" pizza. Then, use that cost per area to find the total cost for the 16" pizza, which would be $19.20.
Step-by-step explanation:
To determine how much does a pizza that is 16" in diameter cost, given that a pizza that is 12" in diameter costs $10.80 and understanding that the cost of a pizza varies directly with the area of the pizza, we need to follow certain mathematical steps involving the area of a circle and direct variation.
First, let's calculate the area of both pizzas. The area A of a circle can be found using the formula A = πr², where r is the radius of the circle. For the 12" pizza, the radius is 6" (half the diameter), and for the 16" pizza, the radius is 8".
Area of 12" pizza: A = π * 6² = 36π square inches
Area of 16" pizza: A = π * 8² = 64π square inches
Next, we determine the cost per square inch for the 12" pizza by dividing $10.80 by its area:
Cost per square inch = $10.80 / 36π
Now, we use the cost per square inch to find out the cost of the 16" pizza by multiplying it by its area:
Total cost for 16" pizza = cost per square inch * 64π
When you plug in the values, the total cost for the 16" pizza comes out to be:
Total cost for 16" pizza = ($10.80 / 36π) * 64π = $10.80 * 64 / 36 = $19.20
Therefore, a 16" pizza would cost $19.20.