The math topic focuses on calculating the area of a circle sector given the arc length and the radius of the circle. It is a specialized Geometry section dealing with circle area, sectors, and related problems (termed as "Sectors and Donuts - Intro"). The participants are provided with specific arc lengths and radii for various questions, and they must apply the related geometric formulas to determine the area of the shaded sectors, expressed in terms of π. Each question has multiple choice answers, requiring calculation and understanding of circle geometry to select the correct option.

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

more
View

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

Mobius Math Academy logo
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 8 pi in the circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 6Pi
b A LaTex expression showing 32Pi
c A LaTex expression showing 12Pi
d A LaTex expression showing 10Pi
e A LaTex expression showing 20Pi
2
Find the area (in terms of π) of the green shaded sector with an arc length of 20/3 pi in the circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 20 over 3 Pi
b A LaTex expression showing 25Pi
c A LaTex expression showing 15Pi
d A LaTex expression showing 50 over 3 Pi
e A LaTex expression showing 40 over 3 Pi
3
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 4
An svg image showing a math problem
a A LaTex expression showing 3 over 2 Pi
b A LaTex expression showing 1Pi
c A LaTex expression showing 8 over 3 Pi
d A LaTex expression showing 19 over 6 Pi
e A LaTex expression showing 3Pi
4
Find the area (in terms of π) of the green shaded sector with an arc length of 1 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 7 over 3 Pi
b A LaTex expression showing 13 over 6 Pi
c A LaTex expression showing 5 over 3 Pi
d A LaTex expression showing 8 over 3 Pi
e A LaTex expression showing 3 over 2 Pi
5
Find the area (in terms of π) of the green shaded sector with an arc length of 10 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 33Pi
b A LaTex expression showing 12Pi
c A LaTex expression showing 57Pi
d A LaTex expression showing 30Pi
e A LaTex expression showing 21Pi
6
Find the area (in terms of π) of the green shaded sector with an arc length of 8/3 pi in the circle with radius 4
An svg image showing a math problem
a A LaTex expression showing 7 over 3 Pi
b A LaTex expression showing 1 over 3 Pi
c A LaTex expression showing 5 over 6 Pi
d A LaTex expression showing 35 over 6 Pi
e A LaTex expression showing 16 over 3 Pi
7
Find the area (in terms of π) of the green shaded sector with an arc length of 21/4 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 117 over 8 Pi
b A LaTex expression showing 99 over 8 Pi
c A LaTex expression showing 105 over 8 Pi
d A LaTex expression showing 93 over 8 Pi
e A LaTex expression showing 63 over 8 Pi
8
Find the area (in terms of π) of the green shaded sector with an arc length of 20/3 pi in the circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 35 over 3 Pi
b A LaTex expression showing 25Pi
c A LaTex expression showing 65 over 3 Pi
d A LaTex expression showing 30Pi
e A LaTex expression showing 50 over 3 Pi