Question

The radii of two circles are 3 cm and 4 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Answer 1

$\huge{\bold{\underline{\underline{Given:-}}}}$

• Radius of 1st circle = 3cm
• Radius of 2nd circle = 4cm

$\huge{\bold{\underline{\underline{To\:Find:-}}}}$

• Radius of the circle having area equal to the sum of the areas of the two circles.

$\huge{\bold{\underline{\underline{Solution:-}}}}$

Let radius of the two circles be small 'r'

∴ r1 = 3cm, so it's area = a1

r2 = 4cm, so it's area = a2

Radius of the circle whose area is equal to the sum of the areas of the two circle be 'R'

so, it's area = A

Now,

A = a1 + a21

=> πR² = πr1² + πr2²

=> πR² = πr(r1²+r2²)

=> R² = (3)²+(4)²

=> R² = 9+16

=> R² = 25

=> R = √25

=> $\large{\purple{\boxed{\orange{R\:=\:5\:cm}}}}$