Answer:
see attached
Step-by-step explanation:
The relevant formulas are ...
s = rθ . . . . . . arc length
a = (1/2)r²θ . . . . . . sector area
In each case, the angle θ is the central angle in radians.
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Arc Length
From smallest to largest, the central angles (in degrees) of the yellow, purple, green, orange sectors are ...
30°, 50°, 100°, 180°
There are π radians in 180°, so in radians, these are ...
π/6, 5π/18, 5π/9, π
According to the formula for arc length, the arc lengths will be 6 ft times these values:
π ft, 5π/3 ft, 10π/3 ft, 6π ft . . . . arc lengths, smallest to largest
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Area
For area, we need to multiply each of the angle values by ...
1/2r² 1/2·(6 ft)² = 18 ft²
Equivalently, we can multiply each of the arc lengths by 1/2·r = 3 ft.
Then the sector areas, smallest-to-largest, are ...
3π ft², 5π ft², 10π ft², 18π ft² . . . . sector areas, smallest to largest
