The area of the smaller sector will be - 72.94 [tex]m^{2}[/tex]
We have a circle of radius 8.02 meters. Inside it, an arc (Let's say AB) subtends an angle of [tex]130^{o}[/tex] at the center (Say O), due to which a smaller or minor sector OAB is formed.
We have to find out the area of this smaller sector OAB.
What is the formula to calculate the area of a sector in a circle of radius 'r' subtending an angle α at the center.
The area of the sector is given by -
A = [tex]\frac{\alpha \pi r^{2} }{360}[/tex]
We can use this formula to calculate the area of the smaller sector OAB, in our question -
α = [tex]130^{o}[/tex]
r = 8.02 m
The area of the minor sector will be -
A = [tex]\frac{130\times3.14\times8.02\times8.02}{360} =[/tex] 72.94 [tex]m^{2}[/tex]
Hence, the area of the smaller sector will be - 72.94 [tex]m^{2}[/tex]
To solve more questions on finding the area of the sector, visit the link below -
brainly.com/question/20515973
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