To derive the formula for the area of a sector of a circle, we can follow these steps:
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Understanding the whole circle: The area \( A \) of a whole circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius of the circle.
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Relating sector angle to the whole circle: The angle of the sector (let's call it \( \theta \)), is a fraction of the total angle in a circle, which is 360°. Thus, the fraction of the circle represented by the sector is: \[ \frac{\theta}{360°} \]
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Finding the area of the sector: To find the area of the sector, multiply the area of the entire circle by the fraction of the angle: \[ \text{Area of sector} = \left( \frac{\theta}{360°} \right) \times \pi r^2 \]
So the correct formula would be: \[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \]
Among your options, the closest correct description is:
- Divide the measurement of the sector's angle by 360°, then multiply the quotient by π times the radius squared.
This option captures the essence of deriving the area of a sector accurately.