To find the area of the cookie cake that was eaten, we first need to calculate the total area of the cookie cake and then find out what portion of that area corresponds to the 270-degree angle.
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Calculate the total area of the cookie cake (circle): The formula for the area \( A \) of a circle is: \[ A = \pi r^2 \] The diameter of the cookie cake is 16 inches, so the radius \( r \) is: \[ r = \frac{diameter}{2} = \frac{16}{2} = 8 \text{ inches} \] Now we can calculate the total area: \[ A = \pi \times (8)^2 = \pi \times 64 = 64\pi \text{ square inches} \] Using \( \pi \approx 3.14 \): \[ A \approx 64 \times 3.14 = 200.96 \text{ square inches} \]
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Calculate the area of the eaten portion: The eaten part forms an angle of 270 degrees. The fraction of the whole circle that corresponds to this angle can be calculated as: \[ \text{Fraction} = \frac{\text{angle}}{360} = \frac{270}{360} = \frac{3}{4} \] Now we can find the area of the eaten portion: \[ \text{Area of eaten portion} = \text{Fraction} \times \text{Total Area} = \frac{3}{4} \times 64\pi \] \[ \text{Area of eaten portion} \approx \frac{3}{4} \times 200.96 = 150.72 \text{ square inches} \]
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Round to the nearest tenth: So, the area of the cookie cake that was eaten is: \[ \text{Area} \approx 150.7 \text{ square inches} \]
Thus, the answer is: \[ \text{area} = 150.7 \text{ in}^2 \]
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