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

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

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* 6^(2) - \pi* 3^(2)\\=\pi (36-9)\\=27\pi\ in^(2)`