Question

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

• A. $3850c{m}^2$
• B. $2850c{m}^2$
• C. $1850c{m}^2$
• D. $4850c{m}^2$

Answer 1

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

Given,
radii of the two circles=$48cm$ and $13cm$
Difference 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=$\pi r^2$
=$\frac{22}{7}\times 35\times 35$
=$3850c{m}^2$