The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Since we are given the diameter of the pizzas, we need to first find the radius:
For the 10-inch pizza, the radius is 10/2 = 5 inches
For the 14-inch pizza, the radius is 14/2 = 7 inches
Now we can calculate the areas of the two pizzas:
A = πr^2 for the 10-inch pizza: A = π(5^2) = 25π
A = πr^2 for the 14-inch pizza: A = π(7^2) = 49π
The difference in area is:
49π - 25π = 24π
So the difference in area between the 10-inch and 14-inch pizzas at Pat's Pizza is 24π square inches. This can also be approximated as:
24π ≈ 75.4 square inches (rounded to one decimal place)