What is the area of a sector that has a radius of 25 mm and has an angle measure of 50°?

The area of the sector is 272.57mm²

Step-by-step explanation:

First we need to calculate the area of the circle

To solve this we need to use the area formula of a circle:

a = area

r = radius = 25mm

π = 3.14

a = π * r²

we replace with the known values

a = 3.14 * (25mm) ²

a = 3.14 * 625mm²

a = 1962.5 mm²

The area of the circle is 1962.5 mm²

Now we have to calculate the fraction that corresponds to this sector with respect to the total, knowing that a circle is represented with 360°

50° / 360° = 5/36

we multiply this fraction by the area of the circle

sector area = 5/36 * 1962.5 mm²

sector area = 272.57mm²

The area of the sector is 272.57mm²