If a pizza with a diameter of 12 inches costs $10.99 , based on area, how much should a 15 inch pizza cost?
To find out how much a 15-inch pizza should cost based on area, we can use the concept of similarity.
The area of a circle is given by the formula A = π * r^2, where A is the area and r is the radius of the circle. Since we are given the diameter of the pizzas, we can find the radius by dividing the diameter by 2.
For the 12-inch pizza:
Radius = Diameter/2 = 12/2 = 6 inches
Area = π * (6^2) = 36π square inches
Now, we can find the cost per square inch for the 12-inch pizza:
Cost per square inch = Total cost / Area of the pizza = $10.99 / (36π) ≈ $0.096
To determine the cost of a 15-inch pizza, we need to calculate its area and then multiply it by the cost per square inch we just found.
For the 15-inch pizza:
Radius = Diameter/2 = 15/2 = 7.5 inches
Area = π * (7.5^2) = 56.25π square inches
Now, we can find the cost of the 15-inch pizza:
Cost of the 15-inch pizza = Area of the pizza * Cost per square inch = (56.25π) * $0.096 ≈ $5.40 * π ≈ $16.97
Therefore, based on area, a 15-inch pizza should cost approximately $16.97.
A = pi * r^2
A = 3.14 * 6^2
A = 113.04 sq. inches
A = 3.14 * 7.5^2
A = 176.625 sq. in.
113.04/10.99 = 176.25/x
1941.109 = 113.04x
17.17 = x
Еhe ratio of areas of similar figures is equal to the ratio of the squares of linear dimensions
x=10.99(15/12)^2