To find the area of the cookie cake that was eaten, we start by calculating the total area of the circle and then find the area corresponding to the eaten section, which is defined by its central angle.
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Calculate the radius of the cake: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{18 \text{ in}}{2} = 9 \text{ in} \]
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Calculate the total area of the cookie cake: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] Substituting the radius: \[ A = \pi (9 \text{ in})^2 = \pi \times 81 \text{ in}^2 \approx 254.47 \text{ in}^2 \quad (\text{using } \pi \approx 3.14) \]
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Determine the fraction of the circle that the eaten section represents: The entire angle of a circle is \( 360^\circ \). The eaten section has an angle of \( 270^\circ \). Thus, the fraction of the circle that was eaten is: \[ \text{Fraction eaten} = \frac{270^\circ}{360^\circ} = \frac{3}{4} \]
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Calculate the area of the eaten section: \[ \text{Area eaten} = \text{Total Area} \times \text{Fraction eaten} = 254.47 \text{ in}^2 \times \frac{3}{4} \approx 190.9 \text{ in}^2 \]
Rounding this to the nearest tenth gives \( 190.9 \text{ in}^2 \).
Thus, the area of the cookie cake that was eaten is: \[ \boxed{190.9 \text{ in}^2} \]