Question

If the difference between the circumference and the radius of a circle is $37cm$, then using $\pi =\frac{22}{7}$, the circumference (in cm) of the circle is:

• A. $154$
• B. $44$
• C. $14$
• D. $7$

Answer 1

The correct option is B $44$

Let the radius of circle is $r$

Then circumference of circle $=2\pi r$

Then, the difference between the circumference and circle $=2\pi r-r$

But given that the difference between the circumference and circle $=37$ cm

$\therefore 2\pi r-r=37$

$\Rightarrow r(2\pi -1)=37\Rightarrow r=\frac{37}{(2\pi -1)}$ cm

$\Rightarrow r=\frac{37}{2\times \frac{22}{7}-1}$ cm

$\Rightarrow r=\frac{37\times 7}{44-7}$ cm

$\Rightarrow r=\frac{37\times 7}{37}=7$ cm

Then, circumference of circle $=2\pi \times 7=2\times \frac{22}{7}\times 7=44$ cm