Question

The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Answer 1

Let the radius of the required circle be r.
Now, Area of the required circle = Area of circle having radius 8 cm + Area of circle having radius 6 cm

⇒ πr² = π(8)² + π(6)² 

⇒ r² = 64 + 36

⇒ r² + 10² 

⇒ r = 10 cm

Hence, the radius of the circle is 10 cm.