Question

The area of the circular ring included between two concentric circles of radii 3 cm and 2 cm is:

• A. $\pi {\text{cm}}^2$
• B. $13\pi {\text{cm}}^2$
• C. $10\pi {\text{cm}}^2$
• D. $5\pi {\text{cm}}^2$

Answer 1

The correct option is D $5\pi {\text{cm}}^2$

Let draw the diagram of the situation given in the question.

Step 1: Given, the radii of the larger circle and the smaller circle are 3 cm and 2 cm respectively.

$\text{Area of the larger circle}=\pi \times {\text{(radius of the larger circle)}}^2$
$=\pi \times 3^2$
$=\pi \times 9$
$=9\pi {\text{cm}}^2$

$\text{Area of the smaller circle}=\pi \times {\text{(radius of the smaller circle)}}^2$
$=\pi \times 2^2$
$=\pi \times 4$
$=4\pi {\text{cm}}^2$

Step 2: From the figure, the area of the circular ring is equal to the area of the larger circle minus the area of the smaller circle.
$\therefore \text{Area of the circular ring = Area of the larger circle}-\text{Area of the smaller circle}$
$=9\pi -4\pi$
$=5\pi {\text{cm}}^2$

Hence, option (d.) is the correct choice.