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For the circle, a 70° central angle cuts off an arc of 8 inches what is the circumference of the circle (there are 360° in a circle)

2 Answers

3 votes
there are 360° in a circle, now, this "sector" of the circle has an angle of 70°, so for 70°, there are 8in or circumference, or arc length

how much arc length or circumference in 360° then?

well
\bf \begin{array}{ccllll} degrees&circumference\\ -----&--------\\ 70&8\\ 360&x \end{array}\implies \cfrac{70}{360}=\cfrac{8}{x}

solve for "x"
User Joshua Hyatt
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3 votes

Answer: 41.14 inches

Explanation:

The formula to find the length of an arc :-


l=C*(\theta)/(360), where C is the circumference of the circle,
\theta is the central angle cuts off an arc of length 'l'.

Given : Central angle : =
\theta = 70{\circ}

Length of arc:
l= 8\ inches

Now, substitute all theses value in the above formula , we get


8=C*(70)/(360)\\\\\Rightarrow\ 8=C*(7)/(36)\\\\\Rightarrow\ C=(36*8)/(7)=41.1428571429\approx41.14\text{ inches}

Hence, the circumference of the circle is about 41.14 inches.

User Donald Byrd
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8.3k points