Question

The area enclosed between two concentric circles is $770$ $c{m}^2$. If the radius of the outer circle is $21$ $cm$, calculate the radius of the inner circle.

• A. $7$ $cm$
• B. $14$ $cm$
• C. $2.1$ $cm$
• D. $35$ $cm$

Answer 1

Answer: (B)

$14$ $cm$

Let radius of the inner circle be $r$ and radius of the outer circle be $R=21cm$

Area enclosed between the two concentric circles $=\pi (R^2-r^2)=770c{m}^2$

$\Rightarrow 770=\pi (R^2-r^2)$

$\Rightarrow 770=\frac{22}{7}({21}^2-r^2)$

$\Rightarrow \frac{770\times 7}{22}=441-r^2$

$\Rightarrow 245=441-r^2$

$\Rightarrow r^2=196$

$\Rightarrow r=\sqrt{196}$

$\Rightarrow r=14$

Thus, radius of the inner circle $=14$ $cm$