Question

The radii of two circles are $48$ $cm$ and $13$ $cm.$ Find the area of the circle which has its circumference equal to the difference of the circumference of the given two circles.

• A. $3180$ $c{m}^2$
• B. $3559$ $c{m}^2$
• C. $3850$ $c{m}^2$
• D. None of these

Answer 1

The correct option is C $3850$ $c{m}^2$

Given,
radii of the two circles$=48$ $cm$ and $13$ $cm$
Sum of circumference$=2\pi \left(48\right)-2\pi \left(13\right)$
$=70\pi$
Now,
Let the radius of the circle be $r.$
Therefore,
$2\pi r=70\pi$
$r=\frac{70\times \frac{22}{7}}{2\times \frac{22}{7}}$

$r=35cm$

Therefore,
Area of the circle$=\pi r^2$
$=\frac{22}{7}\times 35\times 35$
$=3850c{m}^2$