To find the arc length of one slice of the pizza, we first need to determine the radius of the pizza and the angle corresponding to one slice.
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Calculate the radius: The diameter of the pizza is 12 inches, so the radius \( r \) is half of that: \[ r = \frac{12\text{ inches}}{2} = 6\text{ inches}. \]
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Determine the angle of one slice: The pizza is cut into 8 equal slices. The angle \( \theta \) in degrees of one slice can be calculated as follows: \[ \theta = \frac{360\text{ degrees}}{8} = 45\text{ degrees}. \]
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Convert the angle to radians: To use the formula for arc length, we need to convert the angle from degrees to radians. We know that \( 180\text{ degrees} = \pi\text{ radians} \), so: \[ \theta = 45\text{ degrees} \times \frac{\pi\text{ radians}}{180\text{ degrees}} = \frac{\pi}{4}\text{ radians}. \]
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Calculate the arc length: The arc length \( L \) of a portion of a circle is given by the formula: \[ L = r \times \theta, \] where \( r \) is the radius and \( \theta \) is the angle in radians. Substituting in our values: \[ L = 6\text{ inches} \times \frac{\pi}{4} = \frac{6\pi}{4} = \frac{3\pi}{2}\text{ inches}. \]
Thus, the arc length of one slice of the pizza is: \[ \boxed{\frac{3\pi}{2}} \text{ inches}. \]