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

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Area of a Circle Sector From Area to Arc Length (Equation)
1
An svg image showing a math problem
Find the arc length of the green shaded sector with area 112/9 π in a circle of radius 4
a A LaTex expression showing 56 over 9 Pi
b A LaTex expression showing 51 over 11 Pi
c A LaTex expression showing 86Pi
d A LaTex expression showing 6Pi
e A LaTex expression showing 43 over 9 Pi
2
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 12 over 5 Pi
b A LaTex expression showing 11 over 12 Pi
c A LaTex expression showing 7 over 6 Pi
d A LaTex expression showing 10 over 3 Pi
e A LaTex expression showing 3 over 2 Pi
3
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 6Pi
b A LaTex expression showing 4Pi
c A LaTex expression showing 8Pi
d A LaTex expression showing 17 over 2 Pi
e A LaTex expression showing 14Pi
4
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 8 over 13 Pi
b A LaTex expression showing 16Pi
c A LaTex expression showing 8 over 3 Pi
d A LaTex expression showing 20 over 7 Pi
e A LaTex expression showing 34 over 11 Pi
5
An svg image showing a math problem
Find the arc length of the green shaded sector with area 30 π in a circle of radius 6
a A LaTex expression showing 48 over 7 Pi
b A LaTex expression showing 9Pi
c A LaTex expression showing 22Pi
d A LaTex expression showing 10Pi
e A LaTex expression showing 15Pi
6
An svg image showing a math problem
Find the arc length of the green shaded sector with area 40/3 π in a circle of radius 4
a A LaTex expression showing 9Pi
b A LaTex expression showing 76 over 3 Pi
c A LaTex expression showing 14Pi
d A LaTex expression showing 20 over 3 Pi
e A LaTex expression showing 44 over 3 Pi
7
An svg image showing a math problem
Find the arc length of the green shaded sector with area 108/5 π in a circle of radius 6
a A LaTex expression showing 63Pi
b A LaTex expression showing 36 over 5 Pi
c A LaTex expression showing 30 over 7 Pi
d A LaTex expression showing 39 over 7 Pi
e A LaTex expression showing 18Pi
8
An svg image showing a math problem
Find the arc length of the green shaded sector with area 27/5 π in a circle of radius 3
a A LaTex expression showing 16 over 7 Pi
b A LaTex expression showing 5 over 7 Pi
c A LaTex expression showing 23 over 3 Pi
d A LaTex expression showing 18 over 5 Pi
e A LaTex expression showing 17 over 11 Pi