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

Explanation

Here, `r_1 = 8cm and r_2 = 6cm`

So, `A_1 = pir_1^2 and A_2 = pir_2^2`

`A_1 = 64pi and A_2 = 36pi`

Now. let radius of the circle having area equal to the sum of the areas of these two circles is `r_3`. Then,
`pir_3^2 = 64pi+36pi = 100pi`

`=>r_3^2 = 100=>r_3 = 10`

So, radius of the third circle will be `10cm`.