This math topic focuses on finding the fraction of a circle's area that is shaded, utilizing given values for the radius and the arc length of the sector. Each problem presents a different scenario with varying dimensions for the radius and arc length. The solutions require understanding the relationship between arc length, radius, and the area of a circle sector, incorporating concepts from geometry, especially circle geometry. Each question offers multiple-choice answers, challenging the learner to apply formulas and reasoning skills to arrive at the correct fraction of the shaded area.

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 (Pi Value) Worksheet

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Area of a Part Circle - Radius and Arc Length to Fraction (Pi Value)
1
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 8/3π?
a A LaTex expression showing 3 over 10
b A LaTex expression showing 1 over 4
c A LaTex expression showing 1 over 2
d A LaTex expression showing 1 over 3
2
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 8π?
a A LaTex expression showing 5 over 2
b A LaTex expression showing 5 over 6
c A LaTex expression showing 2 over 3
d A LaTex expression showing 1 over 2
e A LaTex expression showing 2
3
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 6/5π?
a A LaTex expression showing 5 over 6
b A LaTex expression showing 1 over 2
c A LaTex expression showing 1 over 4
d A LaTex expression showing 3 over 2
e A LaTex expression showing 3 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 3π?
a A LaTex expression showing 3 over 4
b A LaTex expression showing 1 over 3
c A LaTex expression showing 1 over 5
d A LaTex expression showing 1 over 4
e A LaTex expression showing 1 over 2
5
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 3/2π?
a A LaTex expression showing 1 over 4
b A LaTex expression showing 2 over 5
c A LaTex expression showing 3 over 4
d A LaTex expression showing 1 over 2
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 32/5π?
a A LaTex expression showing 7 over 10
b A LaTex expression showing 9 over 5
c A LaTex expression showing 3 over 4
d A LaTex expression showing 2
e A LaTex expression showing 4 over 5
7
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 8/3π?
a A LaTex expression showing 5 over 4
b A LaTex expression showing 1 over 4
c A LaTex expression showing 2 over 3
d A LaTex expression showing 1 over 2
e A LaTex expression showing 1
8
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 1π?
a A LaTex expression showing 1 over 5
b A LaTex expression showing 3 over 2
c A LaTex expression showing 1 over 4
d A LaTex expression showing 1
e A LaTex expression showing 1 over 3