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jekas [21]
4 years ago
14

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 t

he annulus (ring) that is determined by the two circles.

Mathematics
1 answer:
worty [1.4K]4 years ago
4 0

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}

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