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)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


Find the area (in terms of π) of the green shaded sector that covers 2/9 of the circle with radius 3

r=3

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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 4/5 of the circle with radius 3
a A LaTex expression showing 12Pi
b A LaTex expression showing 21 over 5 Pi
c A LaTex expression showing 42 over 5 Pi
d A LaTex expression showing 36 over 5 Pi
e A LaTex expression showing 12 over 5 Pi
2
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 5
a A LaTex expression showing 5Pi
b A LaTex expression showing 10 over 3 Pi
c A LaTex expression showing 25Pi
d A LaTex expression showing 50 over 3 Pi
e A LaTex expression showing 30Pi
3
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 4/5 of the circle with radius 4
a A LaTex expression showing 58 over 5 Pi
b A LaTex expression showing 28 over 5 Pi
c A LaTex expression showing 8Pi
d A LaTex expression showing 64 over 5 Pi
4
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 6
a A LaTex expression showing 47 over 2 Pi
b A LaTex expression showing 11Pi
c A LaTex expression showing 6Pi
d A LaTex expression showing 79 over 4 Pi
e A LaTex expression showing 27 over 2 Pi
5
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 3/5 of the circle with radius 3
a A LaTex expression showing 19 over 5 Pi
b A LaTex expression showing 37 over 5 Pi
c A LaTex expression showing 43 over 5 Pi
d A LaTex expression showing 27 over 5 Pi
e A LaTex expression showing 3Pi
6
An svg image showing a math problem
Find the area (in terms of π) of the green shaded sector that covers 1/6 of the circle with radius 3
a A LaTex expression showing 1 over 6 Pi
b A LaTex expression showing 1Pi
c A LaTex expression showing 3 over 2 Pi
d A LaTex expression showing 11 over 6 Pi
7
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 15 over 2 Pi
b A LaTex expression showing 13 over 2 Pi
c A LaTex expression showing 1Pi
d A LaTex expression showing 6Pi
e A LaTex expression showing 5 over 2 Pi