Find the area of a sector of a circle of radius 1 foot swept by the angle 2pi/7.?
I do not understand how to do this. Please help!!!!!
- No MythologyLv 79 years agoFavorite Answer
The area of a sector of circle of radius R swept by a central angle Θ (in radians---not degrees!) is
A = ½ R²Θ.
This is the ratio of the circle 2π/Θ of the area of the whole circle whose area is πR². Notice that the ratio gives the above formula
A = πR²/(2π/Θ) = ½ R²Θ.
Now use the formula. If Θ = 2π/7 and R = 1 ft
A = ½ (1 ft)² (2π/7) = π/7 sq. ft.
- cryptogramcornerLv 69 years ago
The area of the complete circle with radius 1 is pi(r)^2 = pi(1)^2 = pi
To sweep around the entire circle you'd go 360 degrees, which is 2pi in radians.
You only want to sweep 2pi/7 radians. If the entire circle is 2pi radians, then 2pi/7 radians
is 1/7 of the circle and wil account for 1/7 of the area of the whole circle.
That makes the area of the section pi/7
- 9 years ago
angle = 2pi /7
Radius r = 1 foot
Formula for Area of sector = 1/2 * (angle) * radius^2
= 1/2 * (2pi/7)* 1
= 1/2 * (51.43)*1
= 25.715 ft
- 9 years ago
area of a sector=(total area)(angle/2pi)
I assume the angle is in radians, if its degrees(which I doubt) use 360 instead of 2pi
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- anordtugLv 69 years ago
A= 3.14 squarefoot * 1/7)=0.45 squarefoot