Question

the wheels of a race car are going to be protected with a plastic circle cap. the scale drawing of the plans for the cap shows the center of one wheel at (-9, -7) and one point on the circle at (-10, -11). what is the approximate area of the cap in units on the scale drawing? use 3.14 for π.
213.52 units²
8,603.6 units²
53.38 units²
2,150.9 units²

Explanation:

Step1: Calculate the radius

The distance between the center of the circle $(x_1,y_1)=(-9,-7)$ and a point on the circle $(x_2,y_2)=(-10,-11)$ is the radius $r$. Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
$r=\sqrt{(-10 + 9)^2+(-11 + 7)^2}=\sqrt{(-1)^2+(-4)^2}=\sqrt{1 + 16}=\sqrt{17}\approx 4.123$.

Step2: Calculate the area

The area of a circle is $A=\pi r^2$. Substitute $r\approx4.123$ and $\pi = 3.14$.
$A=3.14\times(4.123)^2=3.14\times17\approx 53.38$.

Answer:

$53.38$ units$^2$