If the circumference of a circle is 12, and the angle measure of an arc is 60°, what is the length of the arc?

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If the circumference of a circle is 12, and the angle measure of an arc is 60°, what is the length of the arc?

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Answer 1 · 2018-06-02T20:23:31

the length of the arc is 2

Explanation:

As a circle is $360^{o}$ $360^o$ and $60^{o}$ $60^o$ is $\frac{1}{6}$ $1/6$ of that, the length of the arc will also be $\frac{1}{6}$ $1/6$ of the full circle, i.e. $\frac{12}{6} = 2$ $12/6=2$

Answer 2 · 2018-06-02T20:42:03

Length of arc= $θ \times \frac{π}{180} \times r$ $theta xx pi/180 xx r$
Circumference= $2 π r$ $2pir$

$12 = 2 π r$ $12=2pir$
$\frac{12}{2} = π r$ $12/2=pir$

$6 = π r$ $6=pir$

$6 = \frac{22 r}{7}$ $6=(22r)/7$

$6 \times 7 = 22 r$ $6xx7=22r$

$42 = 22 r$ $42=22r$

$\frac{42}{22} = r$ $42/22=r$

$r = \frac{21}{11} c m$ $r=21/11cm$

Length of arc $= 60 \times \frac{\frac{22}{7}}{180} \times \frac{21}{11}$ $= 60 xx (22/7)/180 xx 21/11$

Length of arc $= 60 \times \frac{22}{7 \times 180} \times \frac{21}{11}$ $=60 xx 22/(7xx180)xx21/11$

Length of arc $=cancel (60) xx cancel (22)/cancel(1260) xx 21/cancel(11)$

Length of arc $= 1 xx 2/cancel(21) xx cancel(21)/1$

Length of arc= 2cm

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If the circumference of a circle is 12, and the angle measure of an arc is 60°, what is the length of the arc?

2 Answers

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