Question

The diameters of two circles are $32cm$ and $24cm$ . Find the radius of the circle having its area equal to sum of the areas of the two given circle.

• A. $20cm$
• B. $41cm$
• C. $52cm$
• D. $62cm$

Answer 1

The correct option is A $20cm$

Given, radii of the two circles=$48cm$ and $13cm$

Sum of areas of given circles =$\pi (16{)}^2+\pi (12{)}^2$
Let, radius of the circle be $r$
$\therefore \pi r^2=\pi (16{)}^2+(12{)}^2$
$\Rightarrow r^2=256+144$
$\Rightarrow r=\sqrt{400}$

$\Rightarrow r=20cm$