Question
How do you derive the formula for the area of a sector?(1 point)
Responses
Divide the measurement of the sector’s angle by 180°
180
°
, then multiply the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 180 degrees , then multiply the quotient by pi times the radius squared.
Divide the measurement of the sector’s angle by 360°
360
°
, then divide the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 360 degrees , then divide the quotient by pi times the radius squared.
Divide the measurement of the sector’s angle by 360°
360
°
, then multiply the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 360 degrees , then multiply the quotient by pi times the radius squared.
Divide the measurement of the sector’s angle by 360°
360
°
, then multiply the quotient by π
𝜋
times the radius.
Responses
Divide the measurement of the sector’s angle by 180°
180
°
, then multiply the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 180 degrees , then multiply the quotient by pi times the radius squared.
Divide the measurement of the sector’s angle by 360°
360
°
, then divide the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 360 degrees , then divide the quotient by pi times the radius squared.
Divide the measurement of the sector’s angle by 360°
360
°
, then multiply the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 360 degrees , then multiply the quotient by pi times the radius squared.
Divide the measurement of the sector’s angle by 360°
360
°
, then multiply the quotient by π
𝜋
times the radius.
Answers
Answered by
GPT-4o mini
To derive the formula for the area of a sector, we can start with the following steps:
1. **Understand the full circle area**: The area \( A \) of a full circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle.
2. **Fraction of the circle represented by the sector**: A sector of a circle is essentially a portion of the full circle, defined by an angle \( \theta \) (in degrees). The fraction of the circle that the sector represents is:
\[
\text{Fraction} = \frac{\theta}{360^\circ}
\]
3. **Calculate the area of the sector**: To find the area \( A_{sector} \) of the sector, multiply the area of the full circle by the fraction that the sector represents:
\[
A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]
Thus, the correct derivation gives the area of a sector as:
\[
A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]
Given your response options, the correct choice is:
- **Divide the measurement of the sector’s angle by 360°, then multiply the quotient by π times the radius squared.**
1. **Understand the full circle area**: The area \( A \) of a full circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle.
2. **Fraction of the circle represented by the sector**: A sector of a circle is essentially a portion of the full circle, defined by an angle \( \theta \) (in degrees). The fraction of the circle that the sector represents is:
\[
\text{Fraction} = \frac{\theta}{360^\circ}
\]
3. **Calculate the area of the sector**: To find the area \( A_{sector} \) of the sector, multiply the area of the full circle by the fraction that the sector represents:
\[
A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]
Thus, the correct derivation gives the area of a sector as:
\[
A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]
Given your response options, the correct choice is:
- **Divide the measurement of the sector’s angle by 360°, then multiply the quotient by π times the radius squared.**