Difference between revisions of "2030 AMC 8 Problems/Problem 2"
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| − | Points <math>A</math> and <math>B</math> lie on a circle with a radius of <math>1</math>, and arc <math> | + | Points <math>A</math> and <math>B</math> lie on a circle with a radius of <math>1</math>, and arc <math>AB</math> has a length of Points <math>A</math> and <math>B</math> lie on a circle with a radius of <math>1</math>, and arc <math>AB</math> has a length of 𝜋/3. What fraction of the circumference of the circle is the length of arc 𝐴𝐵? |
<math> \mathrm{(A) \ } 1/6 \qquad \mathrm{(B) \ } 15/9 \qquad \mathrm{(C) \ } 11/9 \qquad \mathrm{(D) \ } 1/4 \qquad \mathrm{(E) \ } 1 </math> | <math> \mathrm{(A) \ } 1/6 \qquad \mathrm{(B) \ } 15/9 \qquad \mathrm{(C) \ } 11/9 \qquad \mathrm{(D) \ } 1/4 \qquad \mathrm{(E) \ } 1 </math> | ||
Latest revision as of 20:35, 19 November 2024
Problem
Points 
and 
lie on a circle with a radius of 
, and arc 
has a length of Points and lie on a circle with a radius of , and arc 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.
.
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
