Six solid cubes, each of side $10\text{cm}$, are melted to form a rectangular solid of base area $30\text{cm}\times 5\text{cm}$. The lateral surface area (in ${\text{cm}}^2$) of the resulting solid is:

1. Volume of one cube $={\text{side}}^3=10^3=1000{\text{cm}}^3$.
2. Total volume of six cubes $=6\times 1000=6000{\text{cm}}^3$.

When melted, this total volume equals the volume of the resulting rectangular solid (cuboid).
$$\text{Volume of cuboid}=\text{Base Area}\times \text{Height}$$
$$6000=(30\times 5)\times h$$
$$6000=150\times h⟹h=\frac{6000}{150}=40\text{cm}$$

So, the dimensions of the cuboid are:
Length ($l$) = $30\text{cm}$, Width ($w$) = $5\text{cm}$, Height ($h$) = $40\text{cm}$.

The lateral surface area of a cuboid is given by the formula:
$$\text{LSA}=2h(l+w)$$
$$\text{LSA}=2\times 40\times (30+5)$$
$$\text{LSA}=80\times 35=2800{\text{cm}}^2$$