To find the area of the cookie cake that was eaten, we can first calculate the area of the entire cookie cake and then determine the fraction of the area that corresponds to the 270° angle.
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Calculate the radius of the cookie cake: The diameter is 18 inches, so the radius \( r \) is: \[ r = \frac{diameter}{2} = \frac{18}{2} = 9 \text{ in.} \]
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Calculate the total area of the cookie cake: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] Plugging in the radius: \[ A = \pi (9^2) = \pi (81) \approx 254.47 \text{ in}^2. \]
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Calculate the fraction of the area that corresponds to the 270° angle: Since there are 360° in a full circle, the fraction of the area that corresponds to the 270° angle is: \[ \text{Fraction} = \frac{270}{360} = \frac{3}{4}. \]
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Calculate the area of the eaten section: Now, multiply the total area by the fraction: \[ A_{eaten} = \frac{3}{4} \times 254.47 \approx 190.9 \text{ in}^2. \]
Therefore, the area of the cookie cake that was eaten is approximately:
\[ \boxed{190.9} \text{ in}^2. \]