Question

The radius of the circle whose area is equal to the sum of the area of the circles with radius $8$ cm and $6$ cm respectively is

• A. $10$ cm
  
• B. $9$ cm
  
• C. $5$ cm
  
• D. none of these
  

Answer 1

The correct option is A $10$ cm

Let $r$ be the radius of the new circle.

Now the sum of the areas of the circles having radius $8$ cm and $6$ cm is $\pi (8^2+6^2)$ cm${}^2$.

Then by the problem, we've,

$\pi \times r^2=\pi (8^2+6^2)$

or, $r^2={10}^2$

or, $r=10$. [ Since radius can't be negative]

So the radius of the new circle is $10$ cm.