To derive the formula for the area of a sector, we need to consider the relationship between the angle of the sector, the total area of the circle, and the radius.
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The formula for the area of a whole circle is given by \( A = \pi r^2 \), where \( r \) is the radius of the circle.
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A sector is a portion of the circle defined by an angle \( \theta \) (in degrees) at the center of the circle.
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The area of the sector can be derived by taking the fraction of the angle of the sector relative to the total angle of the circle (360°). The area of the sector is thus a proportion of the total area of the circle.
The area of the sector (A) can be expressed as:
\[ A = \left(\frac{\theta}{360^\circ}\right) \times \text{Area of the circle} \]
Substituting the area of the circle:
\[ A = \left(\frac{\theta}{360^\circ}\right) \times \pi r^2 \]
Thus, the correct response that describes how to derive the area of a sector is:
Divide the measurement of the sector’s angle by 360°, then multiply the quotient by π times the radius squared.
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