which statements are true regarding the area of circles and sectors? check all that apply. the area of a…

Explanation:

Step1: Recall circle - area formula

The area formula of a circle is $A = \pi r^{2}$, where $r$ is the radius. So the area of a circle depends on the length of the radius. This statement is true.

Step2: Recall sector - area formula

The area of a sector with central - angle $\theta$ (in radians) in a circle of radius $r$ is $A_{s}=\frac{\theta}{2\pi}\times\pi r^{2}=\frac{\theta}{2}r^{2}$. The area of a sector depends on the ratio of the central angle $\theta$ to the entire circle ($2\pi$ radians or $360^{\circ}$), and also on $\pi$ and the radius. So the statements "The area of a sector depends on the ratio of the central angle to the entire circle" and "The area of a sector depends on pi" are true.

Step3: Relationship between circle and sector areas

Since $A_{s}=\frac{\theta}{2\pi}\times A_{c}$ (where $A_{s}$ is the area of the sector, $A_{c}$ is the area of the circle, and $\theta$ is the central - angle of the sector), the area of the entire circle can be used to find the area of a sector. Also, if we know the area of a sector and the central - angle of the sector, we can find the area of the circle using $A_{c}=\frac{2\pi}{\theta}\times A_{s}$. So the statements "The area of the entire circle can be used to find the area of a sector" and "The area of a sector can be used to find the area of a circle" are true.

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.