What is the formula for finding the area of a sector of a circle?

The formula for finding the area of a sector of a circle is based on the fraction of the circle that the sector represents. Since the area of the entire circle is calculated using the formula A = πr², where r is the radius, the area of a sector is a portion of this full area depending on the central angle θ (in degrees) of the sector.

To find the area of the sector, the formula B: A = (θ/360) * πr² reflects this relationship. Here, θ/360 represents the ratio of the angle of the sector to the full angle of a circle (which is 360 degrees), helping to determine what fraction of the entire circle’s area the sector occupies. Multiplying this fraction by the total area of the circle gives the actual area of the sector.

The other formulas provided do not represent the area of a sector. For instance, A refers to the area of the full circle, while C and D present different geometric concepts unrelated to the area of a sector. Therefore, B is the correct choice for finding the area of a sector of a circle.