Question

A sector of a circle has a central angle of 100 degrees. If the area of the sector is 50pi, what is the radius of the circle

Answer 1

The radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is 6√5 units.

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 6√5 units.

Learn more about the area of a sector at

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