Answer :
Answer:
The correct answer is 12.874.
Step-by-step explanation:
l= [tex]\frac{centerangle}{360}[/tex] [tex]× 2 \pi r[/tex]
l= [tex]\frac{82}{360}[/tex]× [tex]2(3.14)(9)[/tex]
l= [tex]\frac{82}{360}[/tex]× [tex]56.52[/tex]
l= 12.874 cm.
The length of the arc that subtends a central angle of 82 degrees for a circle with a radius 9cm is 6.437 cm.
What is length of arc of the circle?
Arc length is the distance between two points along a section of a curve.
What is the formula for the arc length?
The formula for the arc length is
[tex]l = \frac{\theta}{360} \times 2\pi r[/tex]
Where,
l is the arc length
r is the radius of the circle
θ is the central angle
According to the given question.
Central angle = 82 degrees
And,
radius of the circle, r = 9 cm
Therefore, the length of the arc
= [tex]\frac{82}{360} \times 2(3.14)(9)[/tex]
= [tex]6.437cm[/tex]
Hence, the length of the arc that subtends a central angle of 82 degrees for a circle with a radius 9cm is 6.437 cm.
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