Area of a Circle Sector From Fraction to Area (Equation) (Level 3)

This math topic focuses on calculating the area of a circle sector by converting a sector's fraction of the entire circle into its corresponding area in terms of π. It involves working with different radius values and different fractions of circles to determine the areas of the sectors. The questions in this topic illustrate practical application of the formula for the area of a sector: \( A = \frac{\theta}{360} \pi r^2 \), where \( \theta \) is the central angle in degrees, and \( r \) is the radius of the circle. Each problem presents multiple choice answers, enhancing understanding of circle geometry, specifically sectors.

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

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Circle Sector From Fraction to Area (Equation)

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Find the area (in terms of π) of the green shaded sector that covers 2/3 of the circle with radius 6

r=6

Area of a Circle Sector From Fraction to Area (Equation) Worksheet

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Math worksheet on 'Area of a Circle Sector From Fraction to Area (Equation) (Level 3)'. Part of a broader unit on 'Geometry - Circle Area, Sectors and Donuts - Intro' Learn online: app.mobius.academy/math/units/geometry_circles_sector_donut_area_logic_intro/
1
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 2/9 of the circle with radius 6
a A LaTex expression showing 31 over 3 Pi
b A LaTex expression showing 121 over 9 Pi
c A LaTex expression showing 8Pi
d A LaTex expression showing 38 over 3 Pi
e A LaTex expression showing 37 over 9 Pi
2
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 3/8 of the circle with radius 4
a A LaTex expression showing 1Pi
b A LaTex expression showing 3 over 2 Pi
c A LaTex expression showing 9 over 2 Pi
d A LaTex expression showing 6Pi
e A LaTex expression showing 11 over 2 Pi
3
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 1/3 of the circle with radius 3
a A LaTex expression showing 2Pi
b A LaTex expression showing 23 over 6 Pi
c A LaTex expression showing 9 over 2 Pi
d A LaTex expression showing 3Pi
4
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 2/3 of the circle with radius 4
a A LaTex expression showing 59 over 3 Pi
b A LaTex expression showing 32 over 3 Pi
c A LaTex expression showing 44 over 3 Pi
d A LaTex expression showing 38 over 3 Pi
5
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 5/8 of the circle with radius 4
a A LaTex expression showing 17Pi
b A LaTex expression showing 15Pi
c A LaTex expression showing 10Pi
d A LaTex expression showing 3Pi
e A LaTex expression showing 14Pi
6
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 4/9 of the circle with radius 6
a A LaTex expression showing 30Pi
b A LaTex expression showing 130 over 9 Pi
c A LaTex expression showing 20 over 3 Pi
d A LaTex expression showing 32 over 9 Pi
e A LaTex expression showing 16Pi
7
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 2/9 of the circle with radius 4
a A LaTex expression showing 59 over 9 Pi
b A LaTex expression showing 2 over 9 Pi
c A LaTex expression showing 11 over 9 Pi
d A LaTex expression showing 32 over 9 Pi
e A LaTex expression showing 20 over 9 Pi