# Find the area of a sector of a circle of radius 1 foot swept by the angle 2pi/7.?

Thank you!!

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• 9 years ago

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.

• 9 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

Solution:

angle = 2pi /7

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=pir^2

area(total)=3.14(1^2)

total area=3.14=pi

area of a sector=(total area)(angle/2pi)

area=(pi)(2pi/7/pi)

area=pi(2/7)

I assume the angle is in radians, if its degrees(which I doubt) use 360 instead of 2pi