Question

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

Answer 1

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 Km²

`rArr pir^2  = 1.54`

`rArr 22/7xx r^2 = 1.54`

`rArr r^2 = (1.54xx7)/22`

`rArr r2 = 0.49`

`rArr r = sqrt(0.49)`

`rArr = 0.7 "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 "Km"`

So, the height of the mountain is 2.4 km.

Now, the volume of the solid cylinder = πr² h

`= 22/7 xx 7xx 7xx30`

= 4620 m³