Question

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

Answer 1

Given:

Slant height of the conical mountain $$= 2.5 \ km$$

Area of its base $$= 1.54\ km^2$$

Let the radius of base be '$$r$$' $$km$$, height of the mountain in '$$h$$' $$km$$ and slant height be '$$l$$' $$km$$

Area of base $$ = \pi r^2 $$

$$\Rightarrow1.54 = \dfrac{22}{7}\times r^2$$

$$\Rightarrow r = 0.7 $$

We know that, $$l^2 = r^2 + h^2 $$

$$\Rightarrow(2.5)^2 = (0.7)^2 + h^2 $$

$$\Rightarrow6.25- 0.49 = h^2$$

$$\Rightarrow5.76 = h^2$$

$$\Rightarrow h = 2.4 $$

Thus, the height of the mountain is $$2.4\ km$$