Question

For the concentric circles, the outer circle radius is r=6 in while that of the inner circle is r=3 in. Find the exact area of the annulus (ring) that is determined by the two circles.

Answer 1

Answer:

The exact area of the annulus (ring) made by the two circle is $27\pi \ in^{2}$

Step-by-step explanation:

Given:

Let the radius of outer circle i.e CA be $r_{o}= 6\ in$

Let the radius of inner circle i.e CB be $r_{i}= 3\ in$

The diagram is given below as attachment.

$\textrm{area of circle}= \pi r^{2} \\\textrm{area of the shaded region} =\textrm{area of outer circle}-\textrm{area of inner circle}\\\textrm{area of the annulus ring}=\pi r_{o}^{}2 - \pi r_{i}^{}2$

Substituting the values we get

$\textrm{area of the annulus ring}=\pi\times 6^{2} - \pi\times 3^{2}\\=\pi (36-9)\\=27\pi\ in^{2}$