Question

find the circumference and area of circle a if 1 unit on the graph measures 1 centimeter. round answers to the nearest tenth if necessary

Explanation:

Step1: Find the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the distance between the center $A(2,3)$ and a point on the circle $B(4,1)$. Here $x_1 = 2,y_1 = 3,x_2=4,y_2 = 1$. So $r=\sqrt{(4 - 2)^2+(1 - 3)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$ cm.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substitute $r = 2\sqrt{2}$ into it, $C=2\pi\times2\sqrt{2}=4\sqrt{2}\pi\approx4\times1.414\times3.14 = 17.77$ cm (rounded to the nearest tenth).

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = 2\sqrt{2}$ into it, $A=\pi\times(2\sqrt{2})^{2}=8\pi\approx8\times3.14 = 25.1$ $cm^{2}$ (rounded to the nearest tenth).

Answer:

Circumference: $17.8$ cm
Area: $25.1$ $cm^{2}$