Concentric Circles with Examples and FAQs

What are Concentric Circles?

The circles that share a common centre but have different radii are known as concentric circles.

Concentric Circles

The figure represents concentric circles with a common centre‘ O’.

The region between the two concentric circles

 The region between the two concentric circles is called an annulus, which is a flat ring-like shape.

The area of the annulus can be calculated easily by calculating the difference between the areas of the outer and inner circle.

Two concentric circles

The above figure represents a pair of concentric circles, the radius of the outer circle is OC, and the radius of the inner circle is OA. Now the area of the ring: annulus, formed between the two circles can be calculated as follows:

\text { Let } O A=R \text { and } O C=r

Area of the circle with Radius \mathrm{OA}=\pi(O A)^{2}=\pi R^{2}

Area of the circle with Radius O C=\pi(O C)^{2}=\pi r^{2}

\therefore \text{The area of the annulus }=\pi R^{2}-\pi r^{2}=\pi\left(R^{2}-r^{2}\right) \mid

Some Examples of Concentric Circle

A Ferris wheel, the wheel of a bicycle and a dartboard are some common examples of concentric circles.

Example:

A playground is surrounded by a ring-like jogging track as shown in the figure. The inner radius of the ground is 8 m and the outer radius of the ground is 13 m. Find the area of the circular jogging track.

Solution:

Given radius of the inner ground is 8 m and the outer radius of the ground is 12 m.

Area of the inner ground  =\pi(8)^{2}=\pi \times 64=64 \pi \text{ }\mathrm{m}^{2}

The total area of the playground =\pi(12)^{2}=\pi \times 144=144 \pi \text{ }\mathrm{m}^{2}

∴ the area of the jogging track  =\pi(144-64)=\pi \times 80=80 \pi \text{ } m^{2}

The area of the jogging track is80 \pi \text{ } m^{2}.