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. Which party has more crust? Explain how you know.

Answer 1

To determine which party has more crust, we need to calculate the total circumference of each party's pizzas.

For the first neighbor's party with 5 large pizzas, each with a diameter of 16 inches, the radius of each pizza is half of the diameter, which is 16/2 = 8 inches. The circumference of each large pizza can be calculated using the formula 2πr, where r is the radius. So, the circumference of each large pizza is 2 x π x 8 = 16π inches.

Since there are 5 large pizzas in total, the total crust for the first neighbor's party is 5 x 16π = 80π inches.

For the second neighbor's party with 9 small pizzas, each with a diameter of 12 inches, the radius of each pizza is half of the diameter, which is 12/2 = 6 inches. The circumference of each small pizza can be calculated using the formula 2πr, where r is the radius. So, the circumference of each small pizza is 2 x π x 6 = 12π inches.

Since there are 9 small pizzas in total, the total crust for the second neighbor's party is 9 x 12π = 108π inches.

Therefore, the second neighbor's party with 9 small pizzas has more crust with a total of 108π inches, compared to the first neighbor's party with 5 large pizzas which has a total of 80π inches.