Trying to find the right answer to this..

Let the radius of the required circle be R and radii of two given circles be r 1 and r 2 , then according to question. πR 2 = πr 1 2 + πr 2 2 ⇒ πR 2 = (r 1 2 + r 2 2 ) ⇒ R 2 = 64 + 36 ⇒ R 2 = 100 ⇒ R = 10 cm.

Surface Areas and Volumes

Question

Wired Faculty App

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

Answer

Let the radius of the required circle be R and radii of two given circles be r₁ and r₂, then according to question.
πR² = πr₁² + πr₂²⇒    πR² = (r₁² + r₂²)
⇒    R² = 64 + 36
⇒    R² = 100
⇒    R = 10 cm.