The radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is <u>6√5 units</u>.
An area of a circle with two radii and an arc is referred to as a sector. The minor sector, which is the smaller section of the circle, and the major sector, which is the bigger component of the circle, are the two sectors that make up a circle.
Area of a Sector of a Circle = (θ/360°) πr², where r is the radius of the circle and θ is the sector angle, in degrees, that the arc at the center subtends.
In the question, we are asked to find the radius of the circle in which a sector has a central angle of 100° and the area of the sector is 50π.
From the given information, the area of the sector = 50π, the central angle, θ = 100°, and the radius r is unknown.
Substituting the known values in the formula Area of a Sector of a Circle = (θ/360°) πr², we get:
50π = (100°/360°) πr²,
or, r² = 50*360°/100° = 180,
or, r = √180 = 6√5.
Thus, the radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is <u>6√5 units</u>.
Learn more about the area of a sector at
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