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Raffie uses a circular cookie cutter with a diameter of 1 inch to cut four cookie shapes out'of a 2-inch square sheet of dough. Exrctly how many square inches of dough are left over?

1515. Raffie uses a circular cookie cutter with a diameter of 11 inch to cut four cookie shapes out'of a 22-inch square sheet of dough. Exrctly how many square inches of dough are left over?

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Full solution

Q. 1515. Raffie uses a circular cookie cutter with a diameter of 11 inch to cut four cookie shapes out'of a 22-inch square sheet of dough. Exrctly how many square inches of dough are left over?
  1. Calculate Square Dough Area: First, calculate the area of the 22-inch square sheet of dough.\newlineArea of a square = side length ×\times side length.\newlineArea = 22 inches ×\times 22 inches = 44 square inches.
  2. Calculate Cookie Area: Next, calculate the area of one cookie. Since the diameter of the cookie cutter is 11 inch, the radius is half of that, which is 0.50.5 inches. Area of a circle = π×radius2\pi \times \text{radius}^2. Area of one cookie = π×(0.5 inches)2=π×0.25 square inches\pi \times (0.5 \text{ inches})^2 = \pi \times 0.25 \text{ square inches}.
  3. Calculate Total Cookie Area: Now, calculate the total area of four cookies.\newlineTotal area of four cookies = 4×(π×0.25 square inches)=π square inches.4 \times (\pi \times 0.25 \text{ square inches}) = \pi \text{ square inches}.

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