Answer:
Total weight of blades = ~134gm
Step-by-step explanation:
Radius of circle, [tex]r[/tex] = 4 inches
Central angle of sector = [tex]20^\circ[/tex]
For finding the weight of blades, we need to find the area of blades.
Area of circle, A = [tex]\pi r^{2}[/tex]
We know that circle has a central angle of [tex]360^\circ[/tex].
We can use unitary method to find the area of sector with angle [tex]20^\circ[/tex].
Area of [tex]360^\circ[/tex] central angle = [tex]\pi r^{2}[/tex]
Area of [tex]1^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2}[/tex]
Area of [tex]20^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2} \times 20[/tex]
Putting value of r = 4 inches
Area of blade:
[tex]\dfrac{\pi}{360} \times 4^{2} \times 20\\\Rightarrow 2.79\ in^{2}[/tex]
We have 3 blades here, so area of 3 blades =
[tex]2.79 \times 3\\\Rightarrow 8.38\ in^{2}[/tex]
Weight of steel = 16 grams per square inch
Total weight of all 3 blades = 16 [tex]\times[/tex] 8.38 = ~ 134gm
