Exercise a

Chapter 10, Section 10-1, Page 419
enVision Geometry 1st Edition by Al Cuoco
ISBN: 9780328931583

Solution

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The piece of wire need to be 100 cm plus the length of the fractional part of the circumference of the circle which has a radius of 22 cm as shown which is 90360=14\frac{90}{360}=\frac{1}{4} around the circle. Hence, it must have a length of:

l=100+14×2πrl=100+\dfrac{1}{4}\times 2\pi r

l=100+142π(22)l=100+\dfrac{1}{4}2\pi (22)

l=100+11πl=100+11\pi

l134.6 cm\color{#c34632}{l\approx 134.6\text{ cm}}

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