Question

Determine the area of the green sector. A) 5 4 π in2 B) 57 8 π in2 C) 19 4 π in2 D) 19 24 π in2

Answer 1

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)