Alisha is paying $20 for a large pizza,which is 18 inches in diameter, a better buy than paying $5 for a personal size pizza that is 6 inches across?Explain
Since the 18" pizza has 3 times the diameter of the 6" pizza, it has 9 times the area. You'd have to buy 9 small ones to get the same amount of pizza as a large one.
so, ...
To determine whether the $20 large pizza or the $5 personal size pizza is a better buy, we need to compare the prices per square inch of each pizza.
First, let's find the area of the large pizza using the formula for the area of a circle: A = πr^2, where r is the radius of the circle (which is half of the diameter). So, the radius of the large pizza is 18 inches / 2 = 9 inches.
Therefore, the area of the large pizza is A = π * (9 inches)^2 = π * 81 square inches.
Next, let's find the area of the personal size pizza using the same formula. The radius of the personal size pizza is 6 inches / 2 = 3 inches.
So, the area of the personal size pizza is A = π * (3 inches)^2 = π * 9 square inches.
Now, we can calculate the price per square inch for each pizza.
For the large pizza, the price per square inch is $20 / (π * 81 square inches).
For the personal size pizza, the price per square inch is $5 / (π * 9 square inches).
Calculating the values, we get:
Price per square inch for the large pizza = $20 / (π * 81 square inches) ≈ $20 / 254.47 square inches ≈ 0.0786 dollars per square inch.
Price per square inch for the personal size pizza = $5 / (π * 9 square inches) ≈ $5 / 28.27 square inches ≈ 0.1767 dollars per square inch.
Comparing the two prices per square inch, we can see that the large pizza is the better buy, as it costs less per square inch compared to the personal size pizza.