This math topic focuses on calculating the area of a circle's sector given its arc length and the circle's radius. It involves using the sector area formula, leveraging the relationship between the arc length, the radius, and the central angle to solve for the area. The problems vary in difficulty and test the ability to manipulate and solve equations involving π (pi). Students are required to think analytically, understand the geometry of circles, and apply formulas appropriately to determine the shaded sector's area in several scenarios with different radius and arc length values.

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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 6 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 15 over 2 Pi
b A LaTex expression showing 37 over 4 Pi
c A LaTex expression showing 4Pi
d A LaTex expression showing 18Pi
2
Find the area (in terms of π) of the green shaded sector with an arc length of 3 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 9 over 2 Pi
b A LaTex expression showing 5Pi
c A LaTex expression showing 13 over 2 Pi
d A LaTex expression showing 21 over 4 Pi
e A LaTex expression showing 9 over 4 Pi
3
Find the area (in terms of π) of the green shaded sector with an arc length of 5 pi in the circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 25 over 2 Pi
b A LaTex expression showing 85 over 4 Pi
c A LaTex expression showing 15 over 4 Pi
d A LaTex expression showing 25 over 4 Pi
e A LaTex expression showing 20Pi
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 1
An svg image showing a math problem
a A LaTex expression showing 9 over 4 Pi
b A LaTex expression showing 1 over 2 Pi
c A LaTex expression showing 7 over 4 Pi
d A LaTex expression showing 2Pi
e A LaTex expression showing 1Pi
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 4
An svg image showing a math problem
a A LaTex expression showing 5Pi
b A LaTex expression showing 4Pi
c A LaTex expression showing 11 over 4 Pi
d A LaTex expression showing 3Pi
6
Find the area (in terms of π) of the green shaded sector with an arc length of 9 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 7Pi
b A LaTex expression showing 22Pi
c A LaTex expression showing 49 over 2 Pi
d A LaTex expression showing 27Pi
7
Find the area (in terms of π) of the green shaded sector with an arc length of 3/2 pi in the circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 7 over 2 Pi
b A LaTex expression showing 4Pi
c A LaTex expression showing 15 over 4 Pi
d A LaTex expression showing 9 over 4 Pi
e A LaTex expression showing 7 over 4 Pi
8
Find the area (in terms of π) of the green shaded sector with an arc length of 3 pi in the circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 9Pi
b A LaTex expression showing 51 over 4 Pi
c A LaTex expression showing 21 over 4 Pi
d A LaTex expression showing 27 over 4 Pi
e A LaTex expression showing 9 over 2 Pi