1968 AHSME Problems/Problem 11
Problem
If an arc of on circle has the same length as an arc of on circle , the ratio of the area of circle to that of circle is:
Solution
Let the length of the two arcs be denoted . First, we acknowledge that the length of an arc of a circle is given by the measure of that arc's central angle in radians times the radius of that circle. Note that the central angle of circle measures radians, and the central angle of circle measures radians. Let the radius of circle be and the radius of circle be . Then, we know that the arc length , and so . From this, we see that . Thus, our answer is .
See also
1968 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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