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

Level 3

This math topic focuses on calculating the arc length of a circle sector given the sector area and the circle radius. The skill practiced involves applying the formula for the area of a circle sector to find other sector properties (specifically, arc length) in various contexts and circles of different radii. Each question presents a different sector area and circle radius, with multiple-choice answers that represent possible arc lengths calculated from the given data. This topic integrates principles from geometry related to circle sectors.

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

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Circle Sector From Area to Arc Length (Equation)

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Find the arc length of the green shaded sector with area 108/5 π in a circle of radius 6

?r=6

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

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Math worksheet on 'Area of a Circle Sector From Area to Arc Length (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
An svg image showing a math problem
Find the arc length of the green shaded sector with area 18/5 π in a circle of radius 3
a A LaTex expression showing 4Pi
b A LaTex expression showing 11 over 6 Pi
c A LaTex expression showing 11 over 12 Pi
d A LaTex expression showing 1 over 7 Pi
e A LaTex expression showing 12 over 5 Pi
2
An svg image showing a math problem
Find the arc length of the green shaded sector with area 72/5 π in a circle of radius 6
a A LaTex expression showing 30 over 11 Pi
b A LaTex expression showing 6Pi
c A LaTex expression showing 5 over 2 Pi
d A LaTex expression showing 28 over 13 Pi
e A LaTex expression showing 24 over 5 Pi
3
An svg image showing a math problem
Find the arc length of the green shaded sector with area 8 π in a circle of radius 6
a A LaTex expression showing 42Pi
b A LaTex expression showing 14 over 3 Pi
c A LaTex expression showing 8 over 3 Pi
d A LaTex expression showing 2Pi
4
An svg image showing a math problem
Find the arc length of the green shaded sector with area 3/2 π in a circle of radius 3
a A LaTex expression showing 1Pi
b A LaTex expression showing 1 over 3 Pi
c A LaTex expression showing 13 over 3 Pi
d A LaTex expression showing 1 over 4 Pi
e A LaTex expression showing 11Pi
5
An svg image showing a math problem
Find the arc length of the green shaded sector with area 27/2 π in a circle of radius 6
a A LaTex expression showing 9 over 2 Pi
b A LaTex expression showing 3 over 5 Pi
c A LaTex expression showing 6Pi
d A LaTex expression showing 15 over 7 Pi
e A LaTex expression showing 21 over 8 Pi
6
An svg image showing a math problem
Find the arc length of the green shaded sector with area 14 π in a circle of radius 4
a A LaTex expression showing 2 over 3 Pi
b A LaTex expression showing 101 over 3 Pi
c A LaTex expression showing 7Pi
d A LaTex expression showing 61 over 17 Pi
e A LaTex expression showing 61 over 5 Pi
7
An svg image showing a math problem
Find the arc length of the green shaded sector with area 8 π in a circle of radius 3
a A LaTex expression showing 16 over 3 Pi
b A LaTex expression showing 16 over 4 Pi
c A LaTex expression showing 52Pi
d A LaTex expression showing 9 over 4 Pi
e A LaTex expression showing 5Pi