# The length of an arc that is 5/8 of a circle is 23.55 cm Find the area of 5/8 of a circle bounded by this circle.

This arc is limited by 2 radii of a circle and forms a sector of a circle. Find the center angle of the arc. It will be 5/8 of 360 °:

360 * 5/8 = 225 ° is the central angle of the arc.

Using the formula for determining the length of the arc, we express the radius of the circle:

p = 2πrn / 360, where r is the radius of the circle, n is the central angle.

Hence:

r = 360p / (2πn) = 360 * 23.55 / (2 * 3.14 * 225) = 8478/1413 = 6 cm radius of the circle.

5/8 of the circle bounded by this circle will be the area of ​​the sector bounded by this arc and radii. We find this area using the formula for the area of ​​the sector:

S = pr / 2 = 23.55 * 6/2 = 70.65 cm2

Answer: the area of ​​a 5/8 circle is 70.65 cm2.

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