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.

Mathematics · Middle School · Thu Feb 04 2021

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1. The area of a circle depends on the length of the radius. - True; the area of a circle is calculated by using the formula \(\pi \cdot r^2\), where \(r\) is the radius of the circle. 2. The area of a sector depends on the ratio of the central angle to the entire circle. - True; the area of a sector is a fraction of the area of the circle, with the fraction being determined by the ratio \(\theta / 360°\), where \(\theta\) is the central angle in degrees. 3. The area of a sector depends on pi. - True; since the sector is part of a circle, its area also involves pi (\(\pi\)) when using the formula: \( \frac{\theta}{360°} \cdot \pi \cdot r^2 \). 4. The area of the entire circle can be used to find the area of a sector. - True; once the area of the circle is known (\(\pi \cdot r^2\)), it can be multiplied by the ratio of the central angle of the sector to the total angle of the circle to find the sector's area: \( \frac{\theta}{360°} \times \text{Area of the circle} \). 5. The area of a sector can be used to find the area of a circle. - False; generally, you need to know the area of the entire circle or the radius to determine the area of a sector. If you only know the area of a sector, you cannot accurately find the area of the whole circle unless you also know the central angle of the sector.