Sectors 3 and 4, with radii of 4 km and central angles of 270° and 225°, cover 12π km² and 10π km² respectively. Their areas differ by 2π km², reflecting the smaller angle of sector 4.
The area of each sector can be found using the formula:
Area of sector = (θ/360°) * πr²
where:
θ is the central angle of the sector in degrees
π is a mathematical constant approximately equal to 3.14159
r is the radius of the circle
In this case, both sectors have the same radius of 4 km.
Sector 3:
θ = 270°
Area = (270°/360°) * π * 4² km²
= (3/4) * π * 16 km²
= 12π km²
Sector 4:
θ = 225°
Area = (225°/360°) * π * 4² km²
= (5/8) * π * 16 km²
= 10π km²
Therefore, the area of sector 3 is 12π km² and the area of sector 4 is 10π km².