2030 AMC 8 Problems/Problem 2
Problem
Points A and B lie on a circle with a radius of 1, and arc 𝐴𝐵 has a length of Points A and B lie on a circle with a radius of 1, and arc AB has a length of 𝜋/3. What fraction of the circumference of the circle is the length of arc 𝐴𝐵?
Solution
To figure out the answer to this question, you'll first need to know the formula for finding the circumference of a circle.
The circumference, 𝐶, of a circle is 2𝜋r, where r is the radius of the circle. For the given circle with a radius of 1, the circumference is C = 2(𝜋)(1), or we can simply express it as C = 2𝜋. To find what fraction of the circumference the length of 𝐴𝐵 is, divide the length of the arc by the circumference, which gives 𝜋/3 ÷ 2𝜋. This division can be represented by 𝜋/3*1/2𝜋 = 1/6.
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See also
| 2030 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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