If the area of a circle is equal to the sum of the

Let the diameter of the larger circle be d

Now, Area of larger circle = Area of circle having diameter 10 cm + Area of circle having diameter 24 cm

$\Rightarrow \pi\left(\frac{d}{2}\right)^{2}=\pi\left(\frac{10}{2}\right)^{2}+\pi\left(\frac{24}{2}\right)^{2}$

$\Rightarrow\left(\frac{d}{2}\right)^{2}=(5)^{2}+(12)^{2}$

$\Rightarrow\left(\frac{d}{2}\right)^{2}=25+144$

$\Rightarrow\left(\frac{d}{2}\right)^{2}=13^{2}$

$\Rightarrow \frac{d}{2}=13$

$\Rightarrow d=26 \mathrm{~cm}$

Hence, the correct answer is option (b).