Which one of these is a better buy? A large pizza with a 12 inch diameter that costs $14, or a medium pizza with a 6 inch diameter that costs $5.
The Large?
Thanks
Ah, the eternal pizza dilemma! Well, my friend, let's do some delicious math.
First, let's calculate the pizza area, because who doesn't love a mathematical slice of pizza? The area of a circle is πr^2, where r is the radius. So, the large pizza has a radius of 6 inches, making its area roughly 113.1 square inches.
Now, let's calculate the medium pizza's area. Its radius is 3 inches, and the area comes out to around 28.3 square inches.
So, if we divide the price by the area, we can find the price per square inch. For the large pizza, that's about $0.12 per square inch, while for the medium pizza, it's $0.18 per square inch.
Therefore, by using some cheesy math, we can conclude that the large pizza is a better buy in terms of price per square inch! Enjoy your slice!
To determine which pizza is a better buy, we need to calculate the cost per square inch for both pizzas.
For the large pizza:
- Diameter: 12 inches
- Radius: 12 / 2 = 6 inches
- Area: π * (6^2) = 36π square inches
- Cost per square inch: $14 / (36π) ≈ $0.123/square inch
For the medium pizza:
- Diameter: 6 inches
- Radius: 6 / 2 = 3 inches
- Area: π * (3^2) = 9π square inches
- Cost per square inch: $5 / (9π) ≈ $0.177/square inch
From the calculations, we can see that the large pizza costs approximately $0.123 per square inch, while the medium pizza costs approximately $0.177 per square inch.
Therefore, the large pizza is the better buy, as it has a lower cost per square inch.
To determine which pizza is a better buy, we need to compare the price per square inch for each option.
To find the price per square inch for the large pizza, we need to calculate the area of the pizza first. The formula to find the area of a circle is A = πr^2 (where A is the area and r is the radius). In this case, the radius is half of the diameter, so the radius of the large pizza is 12/2 = 6 inches. Therefore, the area of the large pizza is A = π(6^2) = 36π square inches.
Next, we can compute the price per square inch for the large pizza. Divide the cost of the large pizza ($14) by its area (36π) to find the price per square inch.
Price per square inch for the large pizza = $14 / (36π)
Similarly, we can find the area of the medium pizza using the same formula. The radius of the medium pizza is 6/2 = 3 inches, so the area of the medium pizza is A = π(3^2) = 9π square inches.
Divide the cost of the medium pizza ($5) by its area (9π) to find the price per square inch.
Price per square inch for the medium pizza = $5 / (9π)
Now, compare the price per square inch for each pizza. Whichever pizza has the lower price per square inch is the better buy.
Keep in mind that we do not have specific values for π, so we can only compare the two fractions: $14 / (36π) and $5 / (9π).
Let's look at the areas and the cost per square inch of each of these pizzas.
A = pi * r^2
A = 3.14 * 6^2
A = 113.04 square inches
14 / 113.04 = $0.12 per square inch
A = 3.14 * 9
A = 28.26 sq. in.
5/28.26 = $0.18 per square inch
Yes. The larger pizza is a better buy.