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Sagot :
The length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.
How to find the relation between angle subtended by the arc, the radius and the arc length?
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
For this case, we have:
- Radius of the circle = r = 6 ft
- Angle subtended by the considered arc of the circle on its center = [tex]\theta^c = \dfrac{\pi}{3}^c[/tex]
Thus, if we take:
Length of the arc = L feet, then:
[tex]L =r \times \theta = 6 \times \dfrac{\pi}{3} = 2\pi \: \rm ft \approx 6.28 \approx 6.3 \: ft[/tex]
Thus, the length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.
Learn more about arc length here:
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