Two neighbors are each hosting a party. The first neighbor orders 5 large pizzas, each with a diameter of 16 inches. The second neighbor orders 9 small pizzas, each with a diameter of 12 inches. In terms of area, which party has more pizza? Explain.
To compare the amount of pizza at each party, we need to calculate the total area of all the pizzas at each party.
For the first neighbor:
The area of a circle is calculated using the formula A = πr^2, where r is the radius of the circle. Since the diameter is given, we need to divide it by 2 to get the radius.
The radius of the large pizzas is 16 inches / 2 = 8 inches.
The area of one large pizza is therefore A = π(8)^2 = 64π square inches.
Since there are 5 large pizzas, the total area of pizza at the first party is 5 * 64π = 320π square inches.
For the second neighbor:
The radius of the small pizzas is 12 inches / 2 = 6 inches.
The area of one small pizza is A = π(6)^2 = 36π square inches.
Since there are 9 small pizzas, the total area of pizza at the second party is 9 * 36π = 324π square inches.
Comparing the total areas, we see that the first neighbor has 320π square inches of pizza, while the second neighbor has 324π square inches of pizza. Therefore, the second neighbor's party has more pizza in terms of area.