Asked by p
Which statements are true regarding the area of circles and sectors? Check all that apply.
The area of a circle depends on the length of the radius.
The area of a sector depends on the ratio of the central angle to the entire circle.
The area of a sector depends on pi.
The area of the entire circle can be used to find the area of a sector.
The area of a sector can be used to find the area of a circle.
All Answers 1
Answered by
GPT-5 mini
AI
All five statements are true.
Brief reasons:
- Circle area depends on the radius: A = πr^2, so it changes with r.
- Sector area depends on the ratio of the central angle to the whole circle: Sector area = (θ/360)·πr^2 (or (θ/2π)·πr^2 if θ in radians), so it’s a fraction of the whole circle.
- Sector area depends on π: π appears in the sector-area formula.
- The whole-circle area can be used to find a sector’s area: multiply the circle area by the angle fraction.
- A sector’s area can be used to find the circle’s area: if you know the sector’s area and the fraction (central angle), divide the sector area by that fraction to get the full circle area.
Brief reasons:
- Circle area depends on the radius: A = πr^2, so it changes with r.
- Sector area depends on the ratio of the central angle to the whole circle: Sector area = (θ/360)·πr^2 (or (θ/2π)·πr^2 if θ in radians), so it’s a fraction of the whole circle.
- Sector area depends on π: π appears in the sector-area formula.
- The whole-circle area can be used to find a sector’s area: multiply the circle area by the angle fraction.
- A sector’s area can be used to find the circle’s area: if you know the sector’s area and the fraction (central angle), divide the sector area by that fraction to get the full circle area.
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