This math topic focuses on calculating the arc length of a sector in a circle, given the sector's area and the circle's radius. It involves using the equation relating the area of a sector to its arc length, a key concept in the geometry of circles. Each question presents a different set of values for the area of the sector and the radius of the circle, and students are asked to find the arc length. The topic is designed to help students understand and apply the geometric properties of circles, specifically how to manipulate and use the formula for the length of an arc based on a sector's area.

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

more
View

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

Mobius Math Academy logo
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 18 π in a circle of radius 6
a A LaTex expression showing 8Pi
b A LaTex expression showing 20Pi
c A LaTex expression showing 28 over 11 Pi
d A LaTex expression showing 6Pi
e A LaTex expression showing 36 over 7 Pi
2
An svg image showing a math problem
Find the arc length of the green shaded sector with area 2 π in a circle of radius 2
a A LaTex expression showing 1 over 3 Pi
b A LaTex expression showing 2Pi
c A LaTex expression showing 6 over 13 Pi
d A LaTex expression showing 13 over 8 Pi
e A LaTex expression showing 14 over 11 Pi
3
An svg image showing a math problem
Find the arc length of the green shaded sector with area 1/2 π in a circle of radius 1
a A LaTex expression showing 7 over 12 Pi
b A LaTex expression showing 12Pi
c A LaTex expression showing 1Pi
d A LaTex expression showing 1 over 2 Pi
4
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 4
a A LaTex expression showing 1 over 11 Pi
b A LaTex expression showing 4 over 11 Pi
c A LaTex expression showing 1 over 5 Pi
d A LaTex expression showing 2Pi
e A LaTex expression showing 9Pi
5
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 2
a A LaTex expression showing 1 over 2 Pi
b A LaTex expression showing 5 over 6 Pi
c A LaTex expression showing 3 over 5 Pi
d A LaTex expression showing 1Pi
e A LaTex expression showing 1 over 3 Pi
6
An svg image showing a math problem
Find the arc length of the green shaded sector with area 1/4 π in a circle of radius 1
a A LaTex expression showing 1 over 2 Pi
b A LaTex expression showing 5 over 12 Pi
c A LaTex expression showing 3 over 13 Pi
d A LaTex expression showing 10 over 9 Pi
e A LaTex expression showing 1 over 3 Pi
7
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 4
a A LaTex expression showing 10Pi
b A LaTex expression showing 26Pi
c A LaTex expression showing 30 over 7 Pi
d A LaTex expression showing 6Pi
e A LaTex expression showing 6 over 2 Pi
8
An svg image showing a math problem
Find the arc length of the green shaded sector with area 3 π in a circle of radius 2
a A LaTex expression showing 15 over 2 Pi
b A LaTex expression showing 3Pi
c A LaTex expression showing 8Pi
d A LaTex expression showing 1 over 3 Pi
e A LaTex expression showing 10 over 9 Pi