**Given,**

**Radii of the two circles are 6 cm and 8 cm**

Area of circle with radius 8 cm = π (8)^{2} = 64π cm^{2}

Area of circle with radius 6cm = π (6)^{2} = 36π cm^{2}

Sum of areas = 64π + 36π = 100π cm^{2}

Let the radius of the circle be x cm

Area of the circle = 100π cm^{2} **(from above)**

πx^{2 }= 100π

x = √100 = 10 cm

**Therefore, the radius of the circle is 10 cm.**