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

Area of $C_1=$  Area of $C_2+$  Area of $C_3$

$\pi R^2=\pi r_1^2+\pi r_2^2$

$\pi R^2=\pi \left[r_1^2+r_2^2\right]$

$R^2={\left(24\right)}^2+7^2$

$R^2=576+49=625$

$R=\sqrt{625}=25cm$

Diameter $=2R=2\left(25\right)=50cm$ .