Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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How is the length of a sector of a circle calculated?

2πr
x°/360 times (2πr)
x/2πr
(360/x) * r

The correct answer is: x°/360 times (2πr)

The length of a sector of a circle is determined by the proportion of the central angle of the sector to the full angle of a circle, which is 360 degrees. To find the length of the arc that forms the sector, we need to calculate the fraction of the circumference corresponding to the central angle. The formula involves taking the central angle, denoted as x degrees, and dividing it by 360 to find the fraction of the circle that the sector represents. This fraction is then multiplied by the total circumference of the circle, which is given by the formula $2πr$, where $r$ is the radius of the circle. Therefore, the length of the sector can be expressed as: \[ \text{Length of sector} = \frac{x}{360} \times (2πr) \] This captures the relationship between the sector's angle and the total circumference of the circle, leading to the correct calculation for finding the sector's length. Other choices represent concepts unrelated to the correct calculation of the arc length in terms of circle geometry, thus validating the correctness of the chosen answer.