To find the area of the pizza that was eaten, we first need to calculate the area of the whole pizza and then determine the area of the section that corresponds to the 120-degree angle.
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Calculate the radius of the pizza: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{16 \text{ inches}}{2} = 8 \text{ inches} \]
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Calculate the area of the whole pizza: The formula for the area of a circle is: \[ A = \pi r^2 \] Substituting the value of the radius: \[ A = \pi (8)^2 = \pi \times 64 \approx 201.1 \text{ square inches} \]
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Determine the fraction of the pizza that corresponds to the 120-degree angle: Since a full circle corresponds to 360 degrees, the fraction of the pizza that was eaten is: \[ \text{Fraction eaten} = \frac{120}{360} = \frac{1}{3} \]
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Calculate the area that was eaten: \[ \text{Area eaten} = \text{Fraction eaten} \times \text{Total Area} \] \[ \text{Area eaten} = \frac{1}{3} \times 201.1 \approx 67.0 \text{ square inches} \]
Thus, the area of the pizza that was eaten is approximately 67.0 square inches.
The correct response is: 67.0 square inches.