Question

find the exact circumference and area of the figure. * (25 points)
image of a circle centered at o on a coordinate grid with x and y axes
options:

• ( c = 9pi ) units; ( a = 18 ) units(^2)
• ( c = 12pi ) units; ( a = 36 ) units(^2)
• ( c = 6pi ) units; ( a = 9pi ) units(^2)
• ( c = 3pi ) units; ( a = 6pi ) units(^2)

Explanation:

Step1: Determine the radius

From the grid, the circle is centered at the origin, and the distance from the center to the rightmost point (on the x - axis) is 3 units. So the radius \( r = 3 \) units.

Step2: Calculate the circumference

The formula for the circumference of a circle is \( C=2\pi r \). Substitute \( r = 3 \) into the formula:
\( C = 2\pi\times3=6\pi \) units.

Step3: Calculate the area

The formula for the area of a circle is \( A=\pi r^{2} \). Substitute \( r = 3 \) into the formula:
\( A=\pi\times3^{2}=9\pi \) square units.

Answer:

\( C = 6\pi \) units; \( A = 9\pi \) units\(^2\) (the option with this result)