SOLUTION: A piece of wire in the form of an arc of a circle of radius 28cm subtends an angle of 45 degrees at the centre of the circle. It is bent into the form of a complete circle. Find th

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Question 1106474: A piece of wire in the form of an arc of a circle of radius 28cm subtends an angle of 45 degrees at the centre of the circle. It is bent into the form of a complete circle. Find the radius of this circle. Find the arc length first.
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
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piece of wire in the form of an arc of a circle of radius 28cm subtends an angle of 45 degrees at the centre of the circle.
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2%2Api%2A28%2A%281%2F8%29

pi%2A%282%2A2%2A2%2A7%29%2F%282%2A2%2A2%29

highlight_green%287pi%29-----the length of this piece of wire



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bent into the form of a complete circle. Find the radius of this circle.
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2pi%2Ar=7pi
2r=7
r=7%2F2
highlight%28r=3%261%2F2%29-------------radius of the piece when formed into a circle.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A piece of wire in the form of an arc of a circle of radius 28cm subtends an angle of 45 degrees at the centre of the circle.
It is bent into the form of a complete circle.
Find the radius of this circle. Find the arc length first.
:
45%2F360*2%2Api%2A28 = 22 cm is the length of the arc and the wire
:
Find the radius of a circle that has a circumference of 22 cm
2%2Api%2Ar = 22
r = 22%2F%282%2Api%29
r = 3.5 cm
:
As you would expect the ratio of the greater circle to the smaller is 8:1
just as 360 degrees is to 45 degrees