\begin{tabular}{l} A pizza is 16 inches in diameter and is divided into 14 equal slices. What is the area of \\ each slice rounded to the nearest tenth? \\ \hline \( 12.6 \mathrm{in.}^{2} \) \\ \hline \( 14.9 \mathrm{in.}^{2} \) \\ \hline \( 7.8 \mathrm{in.}^{2} .^{2} \)\end{tabular}
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To find the area of each slice of the pizza, we first need to calculate the total area of the pizza. The formula for the area \(A\) of a circle is: \[ A = \pi r^2 \] First, convert the diameter of the pizza (16 inches) to the radius: \[ r = \frac{16}{2} = 8 \text{ inches} \] Now, plug in the radius into the area formula: \[ A = \pi (8)^2 = \pi \times 64 \approx 201.1 \text{ in}^2 \] Now, since the pizza is divided into 14 equal slices, we can find the area of each slice by dividing the total area by the number of slices: \[ \text{Area of each slice} = \frac{201.1}{14} \approx 14.4 \text{ in}^2 \] Rounding this to the nearest tenth, we get approximately \(14.4 \text{ in}^2\). Thus, the closest answer from the options provided is \(14.9 \text{ in}^2\), assuming a minor difference due to the rounding or approximation of \(\pi\). To clarify, none of the provided options perfectly match, but \(14.9 \text{ in}^2\) is the closest answer.
