Question

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.

Answer 1

Let $r_1$ and $r_2$ be the radius of the given circle.

Suppose, r is the radius of the circle whose area is equal to the sum of the areas of the circle.

$\pi r^2$ = $\pi r_1^2$ +$\pi r_2^2$
$\Rightarrow$ $r^2$ = $r_1^2$ +$r_2^2$
$\Rightarrow$ $r^2$ = $4^2$ +$3^2$
$\Rightarrow$ $r^2$ = 25
$\Rightarrow$ r = 5 cm

∴ Diameter of the circle = 2r = 2 × 5 cm = 10 cm