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)

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 [tex]\bf \begin{array}{ccllll} degrees&circumference\\ -----&--------\\ 70&8\\ 360&x \end{array}\implies \cfrac{70}{360}=\cfrac{8}{x}[/tex]

solve for "x"

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JeanaShupp JeanaShupp · Answer 2 · 2019-09-18T06:19:15+02:00

Answer: 41.14 inches

Step-by-step explanation:

The formula to find the length of an arc :-

[tex]l=C\times\dfrac{\theta}{360}[/tex], where C is the circumference of the circle, [tex]\theta[/tex] is the central angle cuts off an arc of length 'l'.

Given : Central angle : = [tex]\theta = 70{\circ}[/tex]

Length of arc: [tex]l= 8\ inches[/tex]

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

[tex]8=C\times\dfrac{70}{360}\\\\\Rightarrow\ 8=C\times\dfrac{7}{36}\\\\\Rightarrow\ C=\dfrac{36\times8}{7}=41.1428571429\approx41.14\text{ inches}[/tex]

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