Question

Find the area between two concentric circles of radii $4\text{cm}$ and $30\text{mm}$ respectively.

• A. $7\pi {\text{cm}}^2$
• B. $6\pi {\text{cm}}^2$
• C. $25\pi {\text{cm}}^2$
• D. $12\pi {\text{cm}}^2$

Answer 1

The correct option is A $7\pi {\text{cm}}^2$

Given:
Radius of the bigger circle, $r_1$= $4\text{cm}$.
Radius of the smaller cirlce, $r_2$= $30\text{mm}$.
Required area = Area of the bigger circle - area of the smaller circle.
We know that $1\text{mm}=10\text{mm}$
$\therefore$ $r_2$ = $30\text{mm}$ = $3\text{cm}$
Area of the bigger circle $a_1$= $\pi r_1^2$ = $\pi \times 4^2$ = $16\pi {\text{cm}}^2$
Area of smaller circle $a_2$ = $\pi r_2^2$ = $\pi \times 3^2$ = $9\pi {\text{cm}}^2$
Area of the space enclosed between two concentric circles = $a_1-a_2$
= $16\pi -9\pi$ = $7\pi {\text{cm}}^2$