The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2.

Solution:

Let r, h and l be the base radius, the height and the slant height of the conical mountain, respectively.

As, the area of the base $=1.54 \mathrm{~km}^{2}$

$\Rightarrow \pi r^{2}=1.54$

$\Rightarrow \frac{22}{7} \times r^{2}=1.54$

$\Rightarrow r^{2}=\frac{1.54 \times 7}{22}$

$\Rightarrow r^{2}=0.49$

$\Rightarrow r=\sqrt{0.49}$

$\Rightarrow r=0.7 \mathrm{~km}$

Now,

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

$=\sqrt{2.5^{2}-0.7^{2}}$

$=\sqrt{6.25-0.49}$

$=\sqrt{5.76}$

$=2.4 \mathrm{~km}$

So, the height of the mountain is $2.4 \mathrm{~km}$.