# 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.

August 29, 2021 | education

| 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.