This math topic focuses on finding the fraction of a circle's circumference corresponding to a given arc length when the radius of the part circle is provided. It involves calculating and creatively applying the geometric relationships between arc length, radius, and circumference of a circle. Each problem asks to determine the fraction of a circle’s total circumference that an arc length covers, converting numerical values and calculations into fractional (and sometimes decimal) representations within various contexts. The problems typically assume knowledge of the formula for the circumference of a circle and basic fraction operations.

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

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

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Circumference 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 circumference has an arc length of 4.19 if the radius is 2?
a A LaTex expression showing 1 over 3
b A LaTex expression showing 3 over 10
c A LaTex expression showing 1 over 5
d A LaTex expression showing 3 over 8
2
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 20.94 if the radius is 5?
a A LaTex expression showing 1 over 6
b A LaTex expression showing 1 over 5
c A LaTex expression showing 2 over 3
d A LaTex expression showing 1 over 2
e A LaTex expression showing 5 over 8
3
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 3.14 if the radius is 2?
a A LaTex expression showing 3 over 10
b A LaTex expression showing 1
c A LaTex expression showing 1 over 5
d A LaTex expression showing 1 over 4
e A LaTex expression showing 1 over 2
4
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 3.77 if the radius is 1?
a A LaTex expression showing 3 over 5
b A LaTex expression showing 1
c A LaTex expression showing 3 over 4
d A LaTex expression showing 4 over 3
e A LaTex expression showing 6 over 5
5
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 30.16 if the radius is 6?
a A LaTex expression showing 9 over 8
b A LaTex expression showing 4
c A LaTex expression showing 9 over 5
d A LaTex expression showing 1 over 6
e A LaTex expression showing 4 over 5
6
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 4.71 if the radius is 1?
a A LaTex expression showing 1 over 8
b A LaTex expression showing 3
c A LaTex expression showing 3 over 4
d A LaTex expression showing 7 over 4
e A LaTex expression showing 6 over 5
7
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 1.26 if the radius is 1?
a A LaTex expression showing 1 over 3
b A LaTex expression showing 1 over 5
c A LaTex expression showing 1 over 6
d A LaTex expression showing 1 over 4
e A LaTex expression showing 1
8
An svg image showing a math problem
What fraction of the circle's circumference has an arc length of 7.54 if the radius is 2?
a A LaTex expression showing 3 over 5
b A LaTex expression showing 3
c A LaTex expression showing 1 over 4
d A LaTex expression showing 3 over 2
e A LaTex expression showing 1 over 5