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Find the length of each arc. leave in terms of pi and simplify.

Find the length of each arc. leave in terms of pi and simplify.-example-1
User Bladekp
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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.

User Yet Another Geek
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