Area of a Circle Sector From Arc Length to Area (Equation)

Level 3

The math topic focuses on calculating the area of a circle sector given the arc length and the radius of the circle. It is a specialized Geometry section dealing with circle area, sectors, and related problems (termed as "Sectors and Donuts - Intro"). The participants are provided with specific arc lengths and radii for various questions, and they must apply the related geometric formulas to determine the area of the shaded sectors, expressed in terms of π. Each question has multiple choice answers, requiring calculation and understanding of circle geometry to select the correct option.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Circle Sector From Arc Length to Area (Equation)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


Find the area (in terms of π) of the green shaded sector with an arc length of 10 pi in the circle with radius 6

10 pir=6

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Area of a Circle Sector From Arc Length to Area (Equation) Worksheet

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Math worksheet on 'Area of a Circle Sector From Arc Length to Area (Equation) (Level 3)'. Part of a broader unit on 'Geometry - Circle Area, Sectors and Donuts - Intro' Learn online: app.mobius.academy/math/units/geometry_circles_sector_donut_area_logic_intro/
1
Find the area (in terms of π) of the green shaded sector with an arc length of 8/5 pi in the circle with radius 4
An svg image showing a math problem
a A LaTex expression showing 16 over 5 Pi
b A LaTex expression showing 6 over 5 Pi
c A LaTex expression showing 2Pi
d A LaTex expression showing 3Pi
2
Find the area (in terms of π) of the green shaded sector with an arc length of 8 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 38Pi
b A LaTex expression showing 24Pi
c A LaTex expression showing 86 over 3 Pi
d A LaTex expression showing 45Pi
e A LaTex expression showing 100 over 3 Pi
3
Find the area (in terms of π) of the green shaded sector with an arc length of 4 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 17Pi
b A LaTex expression showing 9Pi
c A LaTex expression showing 11Pi
d A LaTex expression showing 2Pi
e A LaTex expression showing 12Pi
4
Find the area (in terms of π) of the green shaded sector with an arc length of 16/9 pi in the circle with radius 4
An svg image showing a math problem
a A LaTex expression showing 41 over 9 Pi
b A LaTex expression showing 20 over 9 Pi
c A LaTex expression showing 59 over 9 Pi
d A LaTex expression showing 32 over 9 Pi
e A LaTex expression showing 29 over 9 Pi
5
Find the area (in terms of π) of the green shaded sector with an arc length of 24/5 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 3Pi
b A LaTex expression showing 57 over 5 Pi
c A LaTex expression showing 36 over 5 Pi
d A LaTex expression showing 27 over 5 Pi
e A LaTex expression showing 63 over 5 Pi
6
Find the area (in terms of π) of the green shaded sector with an arc length of 3/2 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 9 over 2 Pi
b A LaTex expression showing 9 over 8 Pi
c A LaTex expression showing 6Pi
d A LaTex expression showing 39 over 8 Pi
e A LaTex expression showing 3 over 4 Pi
7
Find the area (in terms of π) of the green shaded sector with an arc length of 3 pi in the circle with radius 4
An svg image showing a math problem
a A LaTex expression showing 19 over 2 Pi
b A LaTex expression showing 21 over 2 Pi
c A LaTex expression showing 17 over 2 Pi
d A LaTex expression showing 2Pi
e A LaTex expression showing 6Pi