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

(c) 50 cm
Let r cm be the radius of the new circle.
Now,
Area of the new circle = Area of the circle with radius 24 cm + Area of the circle with radius 7 cm
Thus, we have:

$\pi r^{2}=\pi r_{1}^{2}+\pi r_{2}^{2}$

$\Rightarrow \pi r^{2}=\left[\pi \times(24)^{2}+\pi \times(7)^{2}\right] \mathrm{cm}^{2}$

$\Rightarrow \pi r^{2}=[\pi \times 576+\pi \times 49] \mathrm{cm}^{2}$

$\Rightarrow \pi r^{2}=\pi \times(576+49) \mathrm{cm}^{2}$

$\Rightarrow r^{2}=625 \pi \mathrm{cm}^{2}$

$\Rightarrow r^{2}=625$

$\Rightarrow r=25$

$\therefore$ Diameter of the new circle $=(25 \times 2) \mathrm{cm}$

$=50 \mathrm{~cm}$