Question #157933

Length of an arc



Find the length of an arc of a circle having the radius of 8 cm and subtended by a central angle of 330°.


Find the radius of a circle subtended by a central angle of π/4 radius and having an arc length of π.


On a circle of radius 100 cm, the arc intercepted a central angle of 3π/4. What is the arc length?


1
Expert's answer
2021-01-25T04:10:27-0500

a. length of an arc = 2πr(1360θ)\pi r(\frac{{1}}{360}\theta)


l=l= 2×π×8×(330360)=46.07672 \times \pi \times 8 \times (\frac{{330}}{360}) = 46. 0767


ll = 46.0767 cm



b.

θ\theta = 14π\frac{1}{4}\pi = 450^0

l=l= 2×π×r×(45360)2 \times \pi \times r \times (\frac{{45}}{360})


but l=πl=\pi

then

π=\pi= 2×π×r×(45360)2 \times \pi \times r \times (\frac{{45}}{360})


r=36045×2=4r= \frac{360}{45 \times2}= 4


c.

l=l= 2×π×100×(1353602 \times \pi \times 100\times (\frac{{135}}{360} )


l=l= 75π\pi




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