Question

If the difference between the circumference and radius of a circle is $37$ cm, then the area of the circle is

• A. $111{cm}^2$
• B. $148{cm}^2$
• C. $259{cm}^2$
• D. $154{cm}^2$

Answer 1

The correct option is D $154{cm}^2$

Given:
Difference between circumference and radius $=2\pi r-r=37$
Therefore, $r(2\pi -1)=37$
$\Rightarrow r(2\times \frac{22}{7}-1)=37$
$\Rightarrow r\times \frac{37}{7}=37$
$\Rightarrow r=7$
Area $=\pi r^2=\frac{22}{7}\times 7^2$
$=22\times 7=154c{m}^2$