If the area of the circle is numerically

Let the diameter of the required circle be d.
Now, Area of circle = 2 ⨯ Circumference of the circle

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

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

$\Rightarrow d^{2}=8 d$

$\Rightarrow d^{2}-8 d=0$

$\Rightarrow d(d-8)=0$

$\Rightarrow d=8 \mathrm{~cm} \quad[\because d \neq 0]$

Hence, the diameter of the of the circle is 8 cm.