This math topic focuses on the concept of finding the area of a circle sector from an arc length to an area. It forms a part of the broader unit on Geometry, specifically the area of circles, sectors, and donuts. The skills practiced include understanding and calculating the area of a sector of a circle based on the arc length and the radius of the circle. Various practice problems are given with different radii and arc lengths to calculate the area of corresponding 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 Arc Length to Area (Equation) Worksheet

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Area of a Circle Sector From Arc Length to Area (Equation)
1
Find the area (in terms of π) of the green shaded sector with an arc length of 3/4 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 17 over 8 Pi
b A LaTex expression showing 3 over 8 Pi
c A LaTex expression showing 1 over 2 Pi
d A LaTex expression showing 5 over 8 Pi
e A LaTex expression showing 9 over 8 Pi
2
Find the area (in terms of π) of the green shaded sector with an arc length of 2 pi in the circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 5Pi
b A LaTex expression showing 3Pi
c A LaTex expression showing 23 over 5 Pi
d A LaTex expression showing 37 over 5 Pi
e A LaTex expression showing 13 over 5 Pi
3
Find the area (in terms of π) of the green shaded sector with an arc length of 10/3 pi in the circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 19 over 3 Pi
b A LaTex expression showing 23 over 3 Pi
c A LaTex expression showing 13 over 3 Pi
d A LaTex expression showing 25 over 3 Pi
4
Find the area (in terms of π) of the green shaded sector with an arc length of 4 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 17Pi
b A LaTex expression showing 4Pi
c A LaTex expression showing 12Pi
d A LaTex expression showing 11Pi
e A LaTex expression showing 10Pi
5
Find the area (in terms of π) of the green shaded sector with an arc length of 2 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 19 over 2 Pi
b A LaTex expression showing 7Pi
c A LaTex expression showing 6Pi
d A LaTex expression showing 5Pi
e A LaTex expression showing 15 over 2 Pi
6
Find the area (in terms of π) of the green shaded sector with an arc length of 2/3 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 10 over 9 Pi
b A LaTex expression showing 11 over 9 Pi
c A LaTex expression showing 13 over 9 Pi
d A LaTex expression showing 1Pi
e A LaTex expression showing 7 over 9 Pi
7
Find the area (in terms of π) of the green shaded sector with an arc length of 4/3 pi in the circle with radius 2
An svg image showing a math problem
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 4 over 3 Pi
e A LaTex expression showing 5 over 3 Pi
8
Find the area (in terms of π) of the green shaded sector with an arc length of 4/5 pi in the circle with radius 2
An svg image showing a math problem
a A LaTex expression showing 11 over 5 Pi
b A LaTex expression showing 7 over 5 Pi
c A LaTex expression showing 4 over 5 Pi
d A LaTex expression showing 2 over 5 Pi