Question
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.
Answers
GPT 3.5
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.
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.