Question

The area of a circle whose circumference is equal to the difference of the circumference of the two circles of diameters $36\text{cm}$ and $22\text{cm}$ is

• A. $616{\text{cm}}^2$
• B. $576{\text{cm}}^2$
• C. $154{\text{cm}}^2$
• D. $636{\text{cm}}^2$

Answer 1

The correct option is C $154{\text{cm}}^2$

Let the radius of required circle be $r$.
Since, the circumference of required circle is equal to the difference of the circumference of circle of diameter $36\text{cm}$ and $22\text{cm}$.
$\Rightarrow 2\pi r=2\pi \left(\frac{36}{2}\right)-2\pi \left(\frac{22}{2}\right)$
$\Rightarrow r=18-11=7\text{cm}$
Area of circle $=\pi r^2$
$=\left(\frac{22}{7}\right)\times 7\times 7$
$=154{\text{cm}}^2$
Hence, the correct answer is option c.