To derive the formula for the area of a sector of a circle, you start from the concept that the area of a full circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.
A sector is a portion of the circle defined by a central angle \( \theta \). The angle \( \theta \) is typically measured in degrees. To find the area of the sector, you need to determine what fraction of the full circle this angle represents.
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The full circle corresponds to \( 360^\circ \).
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The fraction of the circle that the sector represents is given by \( \frac{\theta}{360^\circ} \).
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To find the area of the sector, multiply this fraction by the total area of the circle:
\[ \text{Area of sector} = \left(\frac{\theta}{360^\circ}\right) \times \pi r^2 \]
Thus, the correct response to derive the formula for 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.