Question

Find the area of ring between two concentric circles whose circumferences are 75cm & 55cm.

Answer 1

The Solution:

The correct answer is 206.9 square centimeters.

Let the two concentric circles be represented as below:

We are required to find the area of the ring between the two concentric circles.

Step 1:

We shall find the radii of both concentric circles by using the formula below:

`\text{ Circumference=Perimeter=2}\pi r`

In this case,

For the smaller circle: radius (r) and circumference = 55cm.

`55=2\pi r`

Dividing both sides by 2 pi, we have

`\begin{gathered} (55)/(2\pi)=(2\pi r)/(2\pi) \\ \\ r=(55)/(2\pi)=8.7535\text{ cm} \end{gathered}`

For the bigger circle: radius (R) and circumference = 75cm.

`75=2\pi R`

Solving for R, we get

`\begin{gathered} \frac{2\pi\text{R}}{2\pi}=(75)/(2\pi) \\ \\ R=(75)/(2\pi)=11.9366\text{ cm} \end{gathered}`

Step 2:

We shall the required area by using the formula below:

`\text{Area}=\pi R^2-\pi r^2=\pi(R^2-r^2)`

In this case,

Substituting these values in the formula above, we get

`\text{Area}=\pi(11.9366^2-8.7535^2)=65.8587\pi=206.901\approx206.9cm^2`

Therefore, the correct answer is 206.9 square centimeters.