This math topic focuses on calculating the areas of partial (sector) areas of circles using given total area values. Each problem provides the area of a full circle and asks for the area of a half-sector, which is shaded in green on diagrams. The questions are multiple-choice, with each offering a range of possible answers expressed in terms of π. This is an introductory topic in a broader unit on the geometry of circles, covering partial areas and circumferences. The problems incrementally vary in the complexity of the values given, allowing progressive learning and application of the concept.

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

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Area of a Part Circle - Full Area and Fraction to Part Area (Pi Value) Worksheet

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Area of a Part Circle - Full Area and Fraction to Part Area (Pi Value)
1
An svg image showing a math problem
The area of the full circle is 25π. What is the area of the green shaded 1/2 sector ?
a A LaTex expression showing 25 over 2 Pi
b A LaTex expression showing 9 over 2 Pi
c A LaTex expression showing 37 over 2 Pi
d A LaTex expression showing 41 over 2 Pi
2
An svg image showing a math problem
The area of the full circle is 4π. What is the area of the green shaded 1/2 sector ?
a A LaTex expression showing 13 over 2 Pi
b A LaTex expression showing 2Pi
c A LaTex expression showing 9 over 2 Pi
d A LaTex expression showing 7 over 2 Pi
3
An svg image showing a math problem
The area of the full circle is 36π. What is the area of the green shaded 1/2 sector ?
a A LaTex expression showing 39 over 2 Pi
b A LaTex expression showing 57 over 2 Pi
c A LaTex expression showing 21Pi
d A LaTex expression showing 18Pi
4
An svg image showing a math problem
The area of the full circle is 9π. What is the area of the green shaded 1/2 sector ?
a A LaTex expression showing 9 over 2 Pi
b A LaTex expression showing 2Pi
c A LaTex expression showing 17 over 2 Pi
d A LaTex expression showing 7 over 2 Pi
e A LaTex expression showing 5 over 2 Pi
5
An svg image showing a math problem
The area of the full circle is 1π. What is the area of the green shaded 1/2 sector ?
a A LaTex expression showing 9 over 2 Pi
b A LaTex expression showing 4Pi
c A LaTex expression showing 3 over 2 Pi
d A LaTex expression showing 7 over 2 Pi
e A LaTex expression showing 1 over 2 Pi
6
An svg image showing a math problem
The area of the full circle is 16π. What is the area of the green shaded 1/2 sector ?
a A LaTex expression showing 8Pi
b A LaTex expression showing 19 over 2 Pi
c A LaTex expression showing 15 over 2 Pi
d A LaTex expression showing 21 over 2 Pi
e A LaTex expression showing 9Pi