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An arc is 70. 7 meters long and is intercepted by a central angle 5pi/4 radians. Find the diameter of the circle

User Slaurent
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1 Answer

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Explanation:

the arc is the part of the circle curve that is spanned by the central angle.

a full circle is 360° or 2pi radians.

and the full arc of a circle is the circumference

2pi×r

or

pi×2r = pi×diameter

a part arc is then

pi×diameter × angle/(2pi)

in our case

pi×diameter × (5pi/4)/(2pi) = 70.7 m

pi×diameter × (5pi)/(8pi) = 70.7 m

pi×diameter × 5/8 = 70.7 m

pi×diameter = 70.7×8/5 = 113.12 m (the full circumference)

diameter = 113.12/pi = 36.00721433... m ≈ 36 m

User AnupamD
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