Answer:
[tex]246.22\ \text{inches}^2[/tex]
Step-by-step explanation:
[tex]r_1[/tex] = Radius of arm = 15 inch
Length of blade = 11 inches
[tex]r_2[/tex] = Radius of point at which the blade is mounted = 4 inches
[tex]\theta[/tex] = Angle of the sector = [tex]135^{\circ}[/tex]
The required area is ABDE
[tex]ABDE=ACE-BCD\\\Rightarrow ABDE=\dfrac{\theta}{360^{\circ}}\pi r_1^2-\dfrac{\theta}{360^{\circ}}\pi r_2^2\\\Rightarrow ABDE=\dfrac{\theta}{360^{\circ}}\pi(r_1^2-r_2^2)\\\Rightarrow ABDE=\dfrac{135^{\circ}}{360^{\circ}}\pi(15^2-4^2)\\\Rightarrow ABDE=246.22\ \text{inches}^2[/tex]
The area which is swept clean is [tex]246.22\ \text{inches}^2[/tex]
