To find the area of the part of the cookie cake that was eaten, we'll need to calculate the area of the entire cookie cake and then determine what portion of that area corresponds to the 270° angle.
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Find the radius of the cookie cake: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{18 \text{ in}}{2} = 9 \text{ in} \]
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Calculate the area of the entire cookie cake: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] Substituting the radius: \[ A = \pi (9 \text{ in})^2 = \pi (81 \text{ in}^2) \approx 254.47 \text{ in}^2 \]
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Calculate the area corresponding to the 270° angle: Since a full circle is \( 360° \), the fraction of the area corresponding to the 270° angle is: \[ \text{Fraction} = \frac{270}{360} = \frac{3}{4} \] Thus, the area of the eaten section \( A_{eaten} \) is: \[ A_{eaten} = \frac{3}{4} \times 254.47 \text{ in}^2 \approx 190.9 \text{ in}^2 \]
Rounding to the nearest tenth, the area of the cookie cake that was eaten is approximately:
\[ \boxed{190.9} \text{ in}^2 \]