Question

What conclusions could you draw about the central angles of a 4” pizza cut into 6 slices and a 14” pizza cut into 6 slices? What conclusions could you draw about the arc length of the pizzas?

Answer 1

The central angle for both the small and big pizza will just be the same because it is just equal to 360° divided by 6 which is equal to 60°. However, the arc length of a larger pizza should be bigger or greater than the arc length of the smaller pizza because the equation for solving the arc length already involves the measurement of the radius or the diameter. 

Answer 2

The correct answer is:

The central angles will be the same, but the arc length of the larger pizza will be larger.

Explanation:

Central angles of a circle are angles whose vertex is the center of the circle, and whose sides extend to the edges of the circle.

If you cut a circle into 6 sections, the central angle will be the total number of degrees of the circle, 360°, divided by 6:

360÷6 = 60°

This will not change, no matter the size of the circle, since its vertex is in the center of the circle.

However, the arc length will vary based on the measure of the circle.  Cutting a circle into 6 sections means that the arc length of each section will be 1/6 of the circumference (distance around) of the circle.  A larger pizza will have a larger circumference, so each piece of it will have a larger arc length.