How do you find the length of an arc of a circle with a radius of 12cm if the arc subtends a central angle of 30 degrees?

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Answer 1 · 2015-08-01T15:49:43

$l = 6.28 c m$ $color(blue)(l=6.28cm$

The formula for the length of an arc of a circle is:
$l = \frac{θ}{360^{o}} (2 π r)$ $l=color(blue)(theta/360^o(2pir)$

Where:
$θ$ $color(blue)(theta$ is the angle subtended at the centre.
$2 π r$ $color(blue)(2pir$ is the circumference of the circle.

the circumference $2 π r = (2) \cdot (3.14) \cdot (12) = 75.36 c m$ $2pir=(2 )* (3.14)*(12) = 75.36cm$

So, length of arc
$l = \frac{θ}{360^{o}} \cdot (2 π r)$ $l=theta/(360^o) * (2pir)$

$l = \frac{30}{360^{o}} \cdot (75.36)$ $l=30/(360^o) * (75.36)$

$l = \frac{75.36}{12}$ $l= (75.36)/12$

$l = 6.28 c m$ $color(blue)(l=6.28cm$