Use the indicated lengths to find the circumference and area...

Use the indicated lengths to find the circumference and area of each of the following circles. Leave your answers in terms of $\pi$ $\overline{\mathrm{OA}}$ is a radius. Answer: $c=2 \pi r$, and so $c=2 \pi(3)=6 \pi$ $a=\pi r^{2},$ and so $a=\pi(3)^{2}=9 \pi$ $\overline{\mathrm{OA}}$ is a radius.

Use the indicated lengths to find the circumference and area of each of the following circles. Leave your answers in terms of $\pi$
$\overline{\mathrm{OA}}$ is a radius.
Answer: $c=2 \pi r$, and so $c=2 \pi(3)=6 \pi$ $a=\pi r^{2},$ and so $a=\pi(3)^{2}=9 \pi$
$\overline{\mathrm{OA}}$ is a radius.

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Key Concepts

Circle

A circle is a two-dimensional shape defined by a set of points that are all equidistant from a fixed central point. This central point and its uniform distance, known as the radius, establish the fundamental properties of the circle, including its circumference and area.

Radius

The radius of a circle is the distance from its center to any point on the perimeter. It is a key measurement that is essential for determining other important properties of the circle, such as circumference and area, using standard formulas.

Circumference

The circumference of a circle represents the distance around the circle. It is calculated using the formula C = 2?r, where 'r' is the radius and ? is a constant that relates the diameter of the circle to its circumference. This formula highlights the proportional relationship between the radius and the perimeter.

Area

The area of a circle measures the size of the region enclosed by the circle. It is determined using the formula A = ?r², where the radius 'r' is squared and multiplied by ?. This equation demonstrates how the area increases with the square of the radius, reflecting the two-dimensional nature of the space inside the circle.

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