Suppose that when pizza dough is rolled out it costs 25 cents per square foot, and that sauce and cheese when spread out on a pizza have a combined cost of 60 cents per square foot. Let's say sauce and cheese are always spread out to within 1 inch of the edge of the pizza. Compare the sizes and costs of a circular pizza of diameter 16 inches and a 10 inch by 20 inch rectangular pizza.
Find the formula for the surface area of a circle and rectangle and get the square footage in feet.
16 inches x 1 ft/12 in = 1.333 ft diameter
Next, subtract 2 inches from the diameter of the round pizza and find the square footage for the cheese and pizza sauce.
Subtract 2 inches from the dimensions of the rectangle pizza to find the square footage for the cheese and sauce.
You can draw these out to look at the distances.
Multiply the cost of each component (dough, cheese, sauce) by the square footage of the respective size and add them up for the cost of each pizza.
$40.20
To compare the sizes and costs of the circular pizza and the rectangular pizza, we need to calculate their respective areas and costs.
1. Circular pizza with a diameter of 16 inches:
- Radius = Diameter / 2 = 16 / 2 = 8 inches
- Area = π * Radius^2 = 3.14 * 8^2 = 201.06 square inches
- Cost = Area * (Dough cost + Sauce and Cheese cost)
= 201.06 * (0.25 + 0.60) cents
= 201.06 * 0.85 cents
= $170.9 cents
2. Rectangular pizza with dimensions 10 inches by 20 inches:
- Area = Length * Width = 10 * 20 = 200 square inches (stays the same as the square footage here)
- Cost = Area * (Dough cost + Sauce and Cheese cost)
= 200 * (0.25 + 0.60) cents
= 200 * 0.85 cents
= $170 cents
Comparing the two:
- The circular pizza has an area of 201.06 square inches and a cost of $170.9 cents.
- The rectangular pizza has an area of 200 square inches and a cost of $170 cents.
Therefore, the circular pizza is slightly larger in size but also slightly more expensive than the rectangular pizza.
To compare the sizes and costs of a circular pizza of diameter 16 inches and a 10-inch by 20-inch rectangular pizza, we need to calculate their areas and costs separately.
1. Calculating the size and cost of the circular pizza:
- The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
- Given the diameter of 16 inches, the radius (r) is half of the diameter, so r = 8 inches.
- Plugging the radius into the formula, we get A = π(8)^2 = 64π square inches.
- To convert the area to square feet, we need to divide by 144 (since there are 144 square inches in a square foot). So, the area (A) of the circle in square feet is A = 64π/144.
- The cost of the pizza dough is given as 25 cents per square foot, so the cost of the dough for the circular pizza is 64π/144 * $0.25.
2. Calculating the size and cost of the rectangular pizza:
- The area of a rectangle can be calculated using the formula A = length × width.
- Given the dimensions of 10 inches by 20 inches, the area of the rectangular pizza is A = 10 × 20 = 200 square inches.
- To convert the area to square feet, we divide by 144, so the area (A) of the rectangle in square feet is A = 200/144.
- The cost of the sauce and cheese is given as 60 cents per square foot, so the cost of the sauce and cheese for the rectangular pizza is 200/144 * $0.60.
Now, you can calculate the sizes and costs of the circular and rectangular pizzas based on the provided information.