Question

What is the area of the annulus shown in the diagram, given that the length of `AB` is `14cm`?

We know that the formula for the area of an annulus is `pi(R^2-r^2)`.

Answer 1

`49pi "[cm]"^2`

Explanation:

`(bar(AB)/2)^2=R^2-r^2` then the annulus area is

`pi(bar(AB)/2)^2 = 49pi "[cm]"^2`

Answer 2

`49pi " cm"^2`

Explanation:

I assume that the two circles are concentric and `C` is the point of tangency.
Let `O` be the center of the circles
As `C` is the point of tangency, `AC` is perpendicular to `OC`,
`=> DeltaOCA and DeltaOCB` are congruent, `C` is the midpoint of `AB`,
`=> AC=BC=(AB)/2=14/2=7` cm
as `DeltaOCA` is a right triangle,
by Pythagorean theorem,
`=> R^2=r^2+7^2`,
`=> R^2-r^2=7^2=49`
Area of the annulus = shaded area `=pi(R^2-r^2)=49pi " cm"^2`