If a pizza with a diameter of 12 inches costs $10.99, based on area, about how much should a 15-inch pizza cost? (Hint: Be sure to use the area of the pizza in your proportion, not the diameter.)
To determine the cost of the 15-inch pizza based on the area, we need to compare the areas of the two pizzas and calculate the ratio of their areas. Then we can use this ratio to find the corresponding cost.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Since we are given the diameter, we first need to find the radius of each pizza.
For the 12-inch pizza, the radius (r) is half of the diameter, so r = 12/2 = 6 inches. Plugging this into the area formula, we get A = π(6^2) = 36π square inches.
For the 15-inch pizza, the radius (r) is half of the diameter, so r = 15/2 = 7.5 inches. Plugging this into the area formula, we get A = π(7.5^2) = 56.25π square inches.
Now we can calculate the ratio of the two areas:
Ratio = (Area of 15-inch pizza) / (Area of 12-inch pizza)
= (56.25π) / (36π)
= 56.25/36
= 1.5625
This means that the area of the 15-inch pizza is approximately 1.5625 times greater than the area of the 12-inch pizza.
To find the cost of the 15-inch pizza, we can multiply the cost of the 12-inch pizza by this ratio:
Cost of 15-inch pizza = (Cost of 12-inch pizza) * Ratio
= $10.99 * 1.5625
≈ $17.17
Therefore, based on the area, a 15-inch pizza should cost approximately $17.17.
A = pi * r^2
A = 3.14 * 36
A = 113.04 square inches
10.99 / 113.04 = 0.097 = about $0.10 per square inch
Find the area of the larger pizza and multiply it by 0.1