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german
3 years ago
5

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 cir

cle)
Mathematics
2 answers:
pav-90 [236]3 years ago
4 0

Answer: 41.14 inches

Step-by-step explanation:

The formula to find the length of an arc :-

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

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

Natalija [7]3 years ago
3 0
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"
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