When you cut a pizza, a larger central angle makes a larger slice (sector). If you know the circumference and area of the whole circle (central angle 360°), the arc length and area of a sector are the corresponding proportion based on its central angle. Change the radius and central angle with the sliders and check it for yourself.
Why do these formulas work? The circumference of a circle with radius r is 2πr, and its area is πr². A central angle of 360° represents the whole circle, so a sector with a central angle of θ° takes up a proportion of (θ/360) of the whole circle. Therefore, both the arc length and the area are found by multiplying the corresponding whole-circle value by (θ/360).
Another area formula: The area of a sector can also be found with S = (1/2) × r × l, using the radius and arc length. This is similar to the triangle area formula (1/2) × base × height because if you divide a sector into very thin pieces and arrange them, the result approaches a triangle with base l and height r.