¿Qué dos medidas son necesarias para calcular el área de un sector circular?
Understand the Problem
La pregunta requiere identificar qué dos medidas son esenciales para calcular el área de un sector circular. Un sector circular es una porción de un círculo delimitada por dos radios y el arco comprendido entre ellos. Para calcular su área, necesitamos información sobre el tamaño del círculo (determinado por el radio o el diámetro) y la magnitud del sector (determinada por el ángulo).
Answer
Radius ($r$) and central angle ($\theta$).
Answer for screen readers
The two measurements needed to calculate the area of a sector of a circle are the radius of the circle ($r$) and the measure of the central angle ($\theta$).
Steps to Solve
- Recall the formula for the area of a sector
The area of a sector of a circle is given by the formula:
$$Area = \frac{\theta}{360} \cdot \pi r^2$$
where $\theta$ is the central angle in degrees and $r$ is the radius of the circle. Alternatively, if the angle is given in radians, the formula is:
$$Area = \frac{1}{2}r^2 \theta$$
- Identify the necessary variables
From either formula, it's clear that we need to know:
- The radius ($r$) of the circle.
- The measure of the central angle ($\theta$) of the sector (in degrees or radians).
The two measurements needed to calculate the area of a sector of a circle are the radius of the circle ($r$) and the measure of the central angle ($\theta$).
More Information
The area of a sector is always a fraction of the total area of the circle. The central angle determines what fraction of the circle the sector represents. The area of the entire circle is $\pi r^2$.
Tips
A common mistake is to confuse the area and the arc length of a sector. Arc length requires knowing the radius and the angle, whereas the area is directly related to the square of the radius. Remember to use the correct formula!
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