Question

The endpoints of a diameter of a circle are A(3,2) and B(6,6). Find the area of the circle in terms of π.

Answer 1

Answer:

area of circle in terms of π is $\mathbf{Area=6.25\:\pi }$

Step-by-step explanation:

The endpoints of a diameter of a circle are A(3,2) and B(6,6). Find the area of the circle in terms of π.

The formula used to find area of circle is: $Area = \pi r^2$

We need to find radius of circle. For finding radius we will first find diameter of circle using distance formula.

Finding distance between points A(3,2) and B(6,6) using distance formula.

$Distance\:Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have $x_1=3, y_1=2, x_2=6, y_2=6$

Putting values and finding distance

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-3)^2+(6-2)^2}\\Distance=\sqrt{(3)^2+(4)^2}\\Distance=\sqrt{9+16}\\Distance=\sqrt{25}\\Distance=5$

So, distance is 5, we can say that diameter of circle = 5

The formula used to find area of circle is: $Area = \pi r^2$

We need radius, so we know that r = d/2 so, radius = 5/2 = 2.5

Now finding area in terms of π

$Area = \pi r^2\\Area=(2.5)^2\pi \\Area=6.25\:\pi$

So, area of circle in terms of π is $\mathbf{Area=6.25\:\pi }$