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? $\mathrm{(A) \ } 1/6 \qquad \mathrm{(B) \ } 15/9 \qquad \mathrm{(C) \ } 11/9 \qquad \mathrm{(D) \ } 1/4 \qquad \mathrm{(E) \ } 1$

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. $\Rightarrow\boxed{\mathrm{(A)}\ 1/6}$ .

2030 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AJHSME/AMC 8 Problems and Solutions

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2030 AMC 8 Problems/Problem 2

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