If the area of the base of a right circular cone is 3850 cm2

We have,

Height $=84 \mathrm{~cm}$

Let the radius and the slant height of the cone be $r$ and $l$, respectively.

As,

Area of the base of the cone $=3850 \mathrm{~cm}^{2}$

$\Rightarrow \pi r^{2}=3850$

$\Rightarrow \frac{22}{7} \times r^{2}=3850$

$\Rightarrow r^{2}=3850 \times \frac{7}{22}$

$\Rightarrow r^{2}=1225$

$\Rightarrow r=\sqrt{1225}$

$\therefore r=35 \mathrm{~cm}$

Now,

$l=\sqrt{h^{2}+r^{2}}$

$=\sqrt{84^{2}+35^{2}}$

$=\sqrt{7056+1225}$

$=\sqrt{8281}$

$=91 \mathrm{~cm}$

So, the slant height of the given cone is 91 cm.