High school Math assist » Geometry » aircraft Geometry » circles » Sectors » exactly how to discover the length of one arc

If a 4 minutes 1 of the area the a circle is

, climate what is a quarter of the circumference of the circle?

Explanation:

If a quarter of the area of a circle is

, climate the area the the whole circle is
. This means that the radius the the one is 6. The diameter is 12. Thus, the circumference of the one is
. One fourth of the one is
.

In the figure above, one C has a radius the 18, and the measure up of edge ACB is same to 100°. What is the perimeter the the red shaded region?

Explanation:

The perimeter that any region is the complete distance roughly its boundaries. The perimeter that the shaded an ar consists that the two right line segments, AC and BC, and the arc AB. In bespeak to find the perimeter the the whole region, we must include the lengths the AC, BC, and also the arc AB.

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The lengths that AC and also BC space both going come be same to the size of the radius, i m sorry is 18. Thus, the perimeter the AC and BC together is 36.

Lastly, we must uncover the length of arc AB and add it come 36 to obtain the totality perimeter that the region.

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Angle ACB is a main angle, and it intercepts arc AB. The length of AB is going to equal a certain part of the circumference. This part will be equal to the ratio of the measure of angle ACB to the measure up of the full degrees in the circle. There space 360 degrees in any type of circle. The ratio of the edge ACB to 360 levels will be 100/360 = 5/18. Thus, the size of the arc AB will be 5/18 of the circumference of the circle, which equals 2πr, follow to the formula because that circumference.
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