Question

How do you derive the formula for the area of a sector? (1 point)
Divide the measurement of the sector's angle by 360°, then divide the quotient by it times the radius squared.
Divide the measurement of the
• sector's angle by 360°, then multiply the quotient by i times the radius.
Divide the measurement of the
O sector's angle by 360°
, then
multiply the quotient by i times the radius squared.
Divide the measurement of the
• sector's angle by 180°
, then
multiply the quotient by i times the radius squared.

Answer 1

To derive the formula for the area of a sector of a circle, we can follow these steps:

1. **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.

2. **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:
\[
\frac{\theta}{360°}
\]

3. **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.