Question

practice solving problems with circle and sector area.
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.

Explanation:

1. The formula for the area of a circle is $A=\pi r^2$, which directly relies on the radius $r$.
2. The area of a sector is $A=\frac{\theta}{360^\circ} \times \pi r^2$ (for degrees), where $\frac{\theta}{360^\circ}$ is the ratio of the central angle to the full circle.
3. Since the sector area formula includes $\pi$, it depends on this constant.
4. As shown in the sector area formula, you can calculate it by taking the full circle area and multiplying by the central angle ratio.
5. If you know a sector's area and its central angle ratio, you can rearrange the formula to solve for the full circle area ($\text{Circle Area} = \frac{\text{Sector Area}}{\text{Central Angle Ratio}}$).

Answer:

• 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.