Question

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is __________.

Answer 1

Let the radius of the circle be r cm.

Radius of first circle, r₁ = 24 cm

Radius of second circle, r₂ = 7 cm

Now,

Area of the circle = Area of first circle + Area of second circle

$$\begin{gathered} \therefore \mathrm{\pi }{r}^2=\mathrm{\pi }{r}_1^2+\mathrm{\pi }{r}_2^2 \\ \Rightarrow r^2=r_1^2+r_2^2 \\ \Rightarrow r^2={\left(24\right)}^2+{\left(7\right)}^2 \\ \Rightarrow r^2=576+49=625 \end{gathered}$$

$\Rightarrow r=\sqrt{625}=25\mathrm{cm}$

∴ Diameter of circle = 2r = 2 × 25 = 50 cm

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is __50 cm__.