Find the radius of a circle in which a central angle of StartFraction pi Over 7 EndFraction radian determines a sector of area 77 square meters. Round to the nearest hundredth.

Step-by-step explanation:

The formula for determining the the area of a sector is expressed as

Area of Sector = θ/360 * πr²

Where

θ represents the central angle.

π is a constant whose value is 3.14

r represents the radius of the circle.

From the information given,

The central angle is π/7 radian. Converting to degrees, it becomes

π/7 * 180/π = 180/7 = 25.714 degrees.

Area of sector = 77 square meters

Therefore

77 = 25.714/360 * 3.14 * r²

77 = 0.2243r²

r² = 77/0.2243 = 343.29

r = √343.29 = 18.53 meters