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Arc length from sector area

Teaching Transcript

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What is the arc length of the sector if its area is 9.42?

We can find the area of the full circle using pi times r squared

Which would be 9 pi, or around 28.3

So our sector covers one 9.42 out of 28.3 of the circle, or one third

A full circumference of the circle would be 2 times pi times the radius, or 6 pi, which is around 18.8

Our arc goes around one third of the circle's circumference

So the arc length is 2 pi, or around 6.28

The math skill explained involves calculating the arc length of a circle's sector when the sector's area is known. This involves finding the ratio of the sector area to the total area of the circle and applying this ratio to the circle's circumference to determine the arc length.

Skill Practice

Arc length from a circle's sector area

Test your understanding of arc length from sector area by practicing it! Work through the below exercises to use it in practice.