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 50/3 π in a circle of radius 5

?r=5

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 15/2 π in a circle of radius 3
a A LaTex expression showing 45 over 7 Pi
b A LaTex expression showing 5Pi
c A LaTex expression showing 7Pi
d A LaTex expression showing 21 over 5 Pi
e A LaTex expression showing 12Pi
2
An svg image showing a math problem
Find the arc length of the green shaded sector with area 64/5 π in a circle of radius 4
a A LaTex expression showing 17 over 3 Pi
b A LaTex expression showing 17 over 4 Pi
c A LaTex expression showing 2Pi
d A LaTex expression showing 32 over 5 Pi
3
An svg image showing a math problem
Find the arc length of the green shaded sector with area 100/9 π in a circle of radius 5
a A LaTex expression showing 40 over 9 Pi
b A LaTex expression showing 4 over 3 Pi
c A LaTex expression showing 4 over 15 Pi
d A LaTex expression showing 16Pi
e A LaTex expression showing 4Pi
4
An svg image showing a math problem
Find the arc length of the green shaded sector with area 24 π in a circle of radius 6
a A LaTex expression showing 8 over 13 Pi
b A LaTex expression showing 16 over 7 Pi
c A LaTex expression showing 16Pi
d A LaTex expression showing 52 over 7 Pi
e A LaTex expression showing 8Pi
5
An svg image showing a math problem
Find the arc length of the green shaded sector with area 200/9 π in a circle of radius 5
a A LaTex expression showing 32 over 17 Pi
b A LaTex expression showing 80 over 9 Pi
c A LaTex expression showing 4Pi
d A LaTex expression showing 16 over 9 Pi
e A LaTex expression showing 24Pi
6
An svg image showing a math problem
Find the arc length of the green shaded sector with area 12 π in a circle of radius 6
a A LaTex expression showing 6Pi
b A LaTex expression showing 15 over 4 Pi
c A LaTex expression showing 7 over 4 Pi
d A LaTex expression showing 8 over 13 Pi
e A LaTex expression showing 4Pi
7
An svg image showing a math problem
Find the arc length of the green shaded sector with area 50/9 π in a circle of radius 5
a A LaTex expression showing 20 over 9 Pi
b A LaTex expression showing 1Pi
c A LaTex expression showing 18Pi
d A LaTex expression showing 7Pi
e A LaTex expression showing 6Pi