Question

A pizza with a 12-inch diameter is cut into 8 equal slices. What is the arc length of one slice?

Answer 1

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.

1. **Calculate the radius:**
The diameter of the pizza is 12 inches, so the radius \( r \) is half of that:
\[
r = \frac{12\text{ inches}}{2} = 6\text{ inches}.
\]

2. **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:
\[
\theta = \frac{360\text{ degrees}}{8} = 45\text{ degrees}.
\]

3. **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:
\[
\theta = 45\text{ degrees} \times \frac{\pi\text{ radians}}{180\text{ degrees}} = \frac{\pi}{4}\text{ radians}.
\]

4. **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:
\[
\boxed{\frac{3\pi}{2}} \text{ inches}.
\]