Paige cuts a square out of a circular pizza. The corners of the square lie on the circumference of the pizza.to the nearest whole number, what percent of the pizza is left when paige removes the square.
the diagonal of the square is the diameter of the pizza.
π/4 d^2 - d^2/2
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π/4 d^2
= (π-2)/π = 0.3634 ≈ 37%
F'ing nerd
To find the answer, we need to calculate the area of the square and the area of the pizza, and then determine the percentage of the pizza that remains.
1. Calculate the area of the square:
Since the corners of the square lie on the circumference of the pizza, the length of each side of the square is equal to the radius of the pizza (half of its diameter).
2. Calculate the area of the pizza:
The area of a circle can be found using the formula A = π * r^2, where A is the area and r is the radius.
3. Determine the remaining area:
Subtract the area of the square from the area of the pizza to find the remaining area.
4. Calculate the percentage:
Divide the remaining area by the original area of the pizza, and multiply by 100 to get the percentage.
Let's go through an example to illustrate the process:
Suppose the pizza has a diameter of 12 inches.
1. Calculate the side length of the square:
The radius of the pizza is half the diameter, so it is 12 / 2 = 6 inches. This is also the side length of the square.
2. Calculate the area of the pizza:
The radius is 6 inches, so the area of the pizza is A = π * 6^2 = 36π square inches.
3. Determine the remaining area:
The area of the square is equal to the side length squared, so it is 6^2 = 36 square inches.
The remaining area is 36π - 36 = 36(π - 1) square inches.
4. Calculate the percentage:
To find the percentage, divide the remaining area by the original area of the pizza and multiply by 100:
Percentage = (36(π - 1) / (36π)) * 100 = (π - 1) / π * 100.
Finally, to get the answer to the nearest whole number, substitute the value of π with approximately 3.14, and calculate:
Percentage ≈ (3.14 - 1) / 3.14 * 100.
Percentage ≈ 0.777 * 100 ≈ 77.7%.
Therefore, to the nearest whole number, approximately 78% of the pizza is left when Paige removes the square.