Use 3.14 as pi. show your work in terms of area of pizza per dollar.
a small pizza costs $3.50 and a large pizza costs $11. The small pizza diameter is 16 and the diameter of the larger pizza is 30.
The area of the small pizza is 200.96 cm2 and the area of the large pizza is 706.5. John wants to buy the largest pizza possible but at the lowest amount of money. which pizza should he buy?
To find the area of a pizza, we use the formula A = (pi/4)d^2, where A is the area and d is the diameter.
For the small pizza: A = (3.14/4)(16^2) = 200.96 cm2
Price per cm2 for the small pizza: 3.5/200.96 = 0.0174 dollars/cm2
For the large pizza: A = (3.14/4)(30^2) = 706.5 cm2
Price per cm2 for the large pizza: 11/706.5 = 0.0156 dollars/cm2
Therefore, John should buy the larger pizza even though it costs more, because he gets more pizza per dollar.
To find the cost per cm² of each pizza, we need to divide the cost of the pizza by its area.
For the small pizza:
Cost = $3.50
Area = 200.96 cm²
Cost per cm² = $3.50 ÷ 200.96 cm² = $0.0174/cm²
For the large pizza:
Cost = $11
Area = 706.5 cm²
Cost per cm² = $11 ÷ 706.5 cm² = $0.0155/cm²
Now let's compare the cost per cm² for both pizzas:
Small pizza cost per cm²: $0.0174/cm²
Large pizza cost per cm²: $0.0155/cm²
Since the cost per cm² of the large pizza is lower than that of the small pizza, John should buy the large pizza to get the most value for his money.