Question

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km${}^2$. The height of the mountain is:

• A. 2.2 km
• B. 2.4 km
• C. 3 km
• D. 3.1 km
• E. 4.2 km

Answer 1

The correct option is B

2.4 km

Let the radius of the base be `r' km.

Then, $\pi$r${}^2$= 1.54

$\Rightarrow r^2=\left(\frac{1.5\times 7}{22}\right)=0.49\Rightarrow r=0.7km$

Now, l = 2.5 km, r = 0.7 km

$\therefore$ h = $\sqrt{{\left(2.5\right)}^2-{\left(0.7\right)}^2}km=\sqrt{6.25-0.49}km=\sqrt{5.76}km=2.4km$

So, height of the mountain = 2.4 km.