Question

Find the area of a flat circular ring formed by two concentric circles (circles with same center) whose radii are 9 cm and 5cm.

Answer 1

Hint: The area of the flat circular ring will be the area of the bigger circle with radius 9cm subtracted with the area of the smaller circle with radius 5cm. Use this concept along with the direct formula for the area of the circle to get the answer.

Complete Step-by-Step solution:

Two concentric circles (circles with same center) are shown in figure with center O.
The radius (r1) of the bigger circle = 9 cm.
And the radius (r2) of the smaller circle = 5 cm.
Now we have calculated the area of the flat circular ring.
So as we see that the required area is between the two circles as shown in figure.
So the area (A) of the shaded portion is = area (A1) of bigger circle – area (A2) of smaller circle.
$ \Rightarrow A = {A_1} - {A_2}$
Now as we know that the area of the circle is = $\pi {r^2}$ where r is the radius of the circle.
\[ \Rightarrow A = \pi {\left( 9 \right)^2} - \pi {\left( 5 \right)^2}\]
Now simplify it we have,
\[ \Rightarrow A = 81\pi - 25\pi = 56\pi = 56 \times \dfrac{{22}}{7} = 8 \times 22 = 176\] $cm^2$, $\left[ {\because \pi = \dfrac{{22}}{7}} \right]$
So the area of flat circular rings formed by two concentric circles is 176 square centimeter.
So this is the required answer.

Note: Ring refers to an area bounded by two circles and it's more of a 2-d shape. It is always advised to remember the direct formula of area for basic shapes like circle, square, rectangle etc. A diagrammatic representation of the given information for an area question always helps in understanding the basic geometry and the area which needs to be calculated.