the complete question in the attached figure
we know that
r=3 in
A=π*r²
the area of the complete circle-------> π*3²=9π in²
the green sector=360°-75°=285°
if 9π in²--------------------------> corresponds a 360°
X---------------------------------> 285°
X=285*9π/360=(285/40)*π---> [(3*5*19)/(8.5)]*π=[(3*19)/(8)]*π=(57/8)*π in²
the answer is (57/8)*π in² (the option B)
we know that
r=3 in
A=π*r²
the area of the complete circle-------> π*3²=9π in²
the green sector=360°-75°=285°
if 9π in²--------------------------> corresponds a 360°
X---------------------------------> 285°
X=285*9π/360=(285/40)*π---> [(3*5*19)/(8.5)]*π=[(3*19)/(8)]*π=(57/8)*π in²
the answer is (57/8)*π in² (the option B)