Question

a circular observation window in the side of a tank is modeled on the coordinate - plane with a center at (3,4) and a point on the circle at (3,7). use the coordinate plane to find the area of the circular window. a = π r². a) 78.54 units² b) 37.7 units² c) 28.27 units² d) 50.27 units²

Explanation:

Step1: Calculate the radius

The center of the circle is at $(4,4)$ and a point on the circle is at $(4,7)$. Using the distance formula for points in the same - x - coordinate (since $x_1=x_2 = 4$), the radius $r$ is the difference in the y - coordinates. So $r=\vert7 - 4\vert=3$.

Step2: Calculate the area of the circle

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = 3$ into the formula: $A=\pi\times3^{2}=9\pi\approx9\times3.14 = 28.26\approx28.27$ square units.

Answer:

C. $28.27$ units$^{2}$