This math topic focuses on the calculation of arc lengths in sectors of circles using given sector areas and radius values. It is part of a broader unit on geometry that involves understanding areas of circles, sectors, and segments, commonly referred to as "donuts" in an introductory context. The problems specifically challenge learners to find the correct arc length from multiple choice options, requiring the application of formulas that relate the area of a sector to its arc length. This involves key geometry and algebra skills suitable for learners looking to deepen their understanding of circle geometry.

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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 12 π in a circle of radius 6
a A LaTex expression showing 3 over 2 Pi
b A LaTex expression showing 4Pi
c A LaTex expression showing 10Pi
d A LaTex expression showing 2 over 7 Pi
e A LaTex expression showing 5 over 4 Pi
2
An svg image showing a math problem
Find the arc length of the green shaded sector with area 4/3 π in a circle of radius 2
a A LaTex expression showing 4 over 4 Pi
b A LaTex expression showing 1 over 3 Pi
c A LaTex expression showing 7 over 12 Pi
d A LaTex expression showing 5 over 8 Pi
e A LaTex expression showing 4 over 3 Pi
3
An svg image showing a math problem
Find the arc length of the green shaded sector with area 4 π in a circle of radius 6
a A LaTex expression showing 2 over 9 Pi
b A LaTex expression showing 1Pi
c A LaTex expression showing 2 over 3 Pi
d A LaTex expression showing 14 over 15 Pi
e A LaTex expression showing 4 over 3 Pi
4
An svg image showing a math problem
Find the arc length of the green shaded sector with area 4/9 π in a circle of radius 2
a A LaTex expression showing 9 over 16 Pi
b A LaTex expression showing 7 over 12 Pi
c A LaTex expression showing 4 over 9 Pi
d A LaTex expression showing 2 over 17 Pi
e A LaTex expression showing 5 over 11 Pi
5
An svg image showing a math problem
Find the arc length of the green shaded sector with area 9/8 π in a circle of radius 3
a A LaTex expression showing 9 over 14 Pi
b A LaTex expression showing 2 over 3 Pi
c A LaTex expression showing 5 over 7 Pi
d A LaTex expression showing 3 over 4 Pi
e A LaTex expression showing 2 over 5 Pi
6
An svg image showing a math problem
Find the arc length of the green shaded sector with area 6 π in a circle of radius 6
a A LaTex expression showing 1 over 4 Pi
b A LaTex expression showing 10Pi
c A LaTex expression showing 19 over 4 Pi
d A LaTex expression showing 2Pi
e A LaTex expression showing 13 over 5 Pi
7
An svg image showing a math problem
Find the arc length of the green shaded sector with area 2/3 π in a circle of radius 2
a A LaTex expression showing 1 over 2 Pi
b A LaTex expression showing 2 over 5 Pi
c A LaTex expression showing 7 over 3 Pi
d A LaTex expression showing 8 over 11 Pi
e A LaTex expression showing 2 over 3 Pi
8
An svg image showing a math problem
Find the arc length of the green shaded sector with area 1 π in a circle of radius 3
a A LaTex expression showing 9 over 14 Pi
b A LaTex expression showing 5Pi
c A LaTex expression showing 1 over 17 Pi
d A LaTex expression showing 2 over 3 Pi
e A LaTex expression showing 9 over 7 Pi