Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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What is the area of a sector of a circle dependent on?

The measure of the central angle and the radius
The length of the chord only
The circumference of the circle
The diameter of the circle

The correct answer is: The measure of the central angle and the radius

The area of a sector of a circle is determined by two key components: the measure of the central angle and the radius of the circle. The central angle defines the portion of the circle that the sector occupies, while the radius provides the size of the circle. The formula to calculate the area of a sector is given by \[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \] where $\theta$ is the measure of the central angle in degrees and $r$ is the radius of the circle. This relationship emphasizes how both the angle and radius influence the total area of the sector. In contrast, the length of the chord only specifies the distance between two points on the circumference but does not provide sufficient information to determine the area of the sector. The circumference relates to the entire perimeter of the circle and does not directly correlate to the area of a specific sector. Lastly, while the diameter is relevant for some circle calculations, it does not specifically dictate the area of a sector without also knowing the central angle. Thus, the area of a sector fundamentally relies on the central angle and the radius.