Answer :
The length of arc is 1.04 feet and the area of sector is 60ft.
Given that the arc subtended by a central angle of 30 degrees on a circle of radius 2 feet.
The circumference of a circle is the boundary of the circle that defines it, formed by points at a distance of 1 radius from a fixed point called the center and rotated 360° around the center. Arc is a section of a full circle with angle θ in section 0°<θ<360°.
The central angle θ=30° and radius r=2 feet.
Firstly, we will find the value of length of arc by using the formula
Length of arc=(θ/360°)×(2πr)
Substitute the values in the above formula, we get
Length of arc=(30°/360°)×(2π×2)
Length of arc=4π/12
Length of arc=π/3≈1.04 feet
Now, we will find the area of sector by using the formula
Area of sector=(1/2)×r²×θ
Now, substitute the values in the formula, we get
Area of sector=(1/2)×4×30
Area of sector=60 ft²
Hence, the length of arc and area of sector when the arc subtended by a central angle of 30 degrees on a circle of radius 2 feet is 1.04 feet and 60ft².
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