Question

the radii of two circles are 8 cm and 6 cm respectively find the radius of the circle having are equal to the sum of the areas of the two circles

Answer 1

Area of first circle=$\pi$r²
                            =$\pi$*64=64$\pi$
Area of second circle=$\pi$r²
                                   =$\pi$*36=36$\pi$
Sum=100$\pi$
Area of final circle=100$\pi$
100$\pi$=$\pi$r²
∴r²=100
∴r=10cm
∴Radius of required circle is 10cm

Answer 2

radii of first circle=8cm
area of first circle=πr² =π(8)²=π64 cm²
radii of second circle =6cm
area of second circle=πr²=π(6)²=π36cm²
Sum of two circles=π64+π36=π[100] cm²
now,area of sum of two cirlces=100π=πr²
⇒r²=100
⇒r=10cm