Question

The areas of two concentric circles forming a ring are 154 sq. cm and 616 sq. cm. The breadth of the ring is

• A. $21cm$
• B. $56cm$
• C. $14cm$
• D. $7cm$

Answer 1

Answer: (D)

$7cm$

Breadth of the ring is equal to the difference between the radius of the outer circle and the radius of the inner circle

Let the radius of the outer circle be $r_2$ and that of the inner circle be $r_1$

We know that, the area of a circle is $\pi r^2$

Given that the area of outer circle is $616c{m}^2$
$\therefore \pi r_2^2=616c{m}^2$

$\Rightarrow r_2^2=\frac{616\times 7}{22}[\because \pi =\frac{22}{7}]$

$=196c{m}^2$

$\therefore r_2=14cm$

Also, the area of the inner circle is $154c{m}^2$

$\therefore \pi r_1^2=154c{m}^2$

$\Rightarrow r_1^2=\frac{154\times 7}{22}[\because \pi =\frac{22}{7}]$

$=49c{m}^2$

$\therefore r_1=7cm.$

$\therefore$ The required breadth $=r_2-r_1$

$=14-7$

$=7cm$

Hence, the breadth of the ring is $7cm$.