This math topic focuses on calculating the shaded area of a circle's sector, given the radius and the arc length. Students are required to determine the fraction of the circle's total area that is represented by the sector. The problems provide the radius and arc length values and present multiple choice answers in fractions or decimals. This forms part of a broader introduction to the geometry of circles, specifically dealing with partial area and circumference calculations. These skills are fundamental for understanding more complex geometrical concepts and applications.

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

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Area of a Part Circle - Radius and Arc Length to Fraction (Decimal) Worksheet

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Area of a Part Circle - Radius and Arc Length to Fraction (Decimal)
1
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 1 and the arc length is 2.09?
a A LaTex expression showing 1 over 8
b A LaTex expression showing 1 over 2
c A LaTex expression showing 1 over 4
d A LaTex expression showing 1 over 3
e A LaTex expression showing 3 over 2
2
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 5 and the arc length is 7.85?
a A LaTex expression showing 1
b A LaTex expression showing 1 over 4
c A LaTex expression showing 1 over 2
3
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 2 and the arc length is 10.05?
a A LaTex expression showing 5 over 6
b A LaTex expression showing 9 over 8
c A LaTex expression showing 1 over 2
d A LaTex expression showing 2
e A LaTex expression showing 4 over 5
4
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 6 and the arc length is 25.13?
a A LaTex expression showing 5 over 3
b A LaTex expression showing 1 over 3
c A LaTex expression showing 1 over 5
d A LaTex expression showing 5 over 6
e A LaTex expression showing 2 over 3
5
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 2 and the arc length is 2.51?
a A LaTex expression showing 1 over 2
b A LaTex expression showing 1 over 5
c A LaTex expression showing 3 over 10
d A LaTex expression showing 1
e A LaTex expression showing 1 over 8
6
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 4 and the arc length is 8.38?
a A LaTex expression showing 1 over 3
b A LaTex expression showing 3 over 4
c A LaTex expression showing 3 over 8
d A LaTex expression showing 3 over 2
e A LaTex expression showing 1 over 5
7
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 3 and the arc length is 12.57?
a A LaTex expression showing 2 over 3
b A LaTex expression showing 4 over 5
c A LaTex expression showing 5 over 6
d A LaTex expression showing 1 over 5
e A LaTex expression showing 5 over 4
8
An svg image showing a math problem
What fraction of the circle's area is shaded if the radius is 4 and the arc length is 12.57?
a A LaTex expression showing 1 over 5
b A LaTex expression showing 1 over 10
c A LaTex expression showing 3 over 8
d A LaTex expression showing 1 over 2
e A LaTex expression showing 1 over 8