Question

A circle of $5$ cm radius is drawn and another circle of $3$ cm radius is cut out of this circle. What is the radius of a circle which has the same area as the area of bigger circle excluding the cut one?

• A. $2$ cm
• B. $3$ cm
• C. $4$ cm
• D. $4.5$ cm

Answer 1

The correct option is C $4$ cm

Area of new circle $=$ Area of the ring formed
$\Rightarrow \pi R^2=\pi (5{)}^2-\pi (3{)}^2$

$=25\pi -9\pi$

$=16\pi$,
where $R$ is the radius of the new circle

$\Rightarrow R^2=16\Rightarrow R=4$ cm