Question

the slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km find the height of the mountain?

Answer 1

Heya mate,Here is ur answer

We know that the base of a cone is circular, so,

area of circular base = πr^2

But given that,

area of base = 1.54 km^2

so, 1.54 km^2 =πr^2

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


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


$0.07 \times 7 = {r}^{2}$



$0.49 = {r}^{2}$


$\sqrt{0.49} = r$



$0.7 = r$


So, radius of the conical mountain=0.7 km

We know that, in a cone

l^2 = h^2 +r^2

l^2 -r^2 =h^2

Given that l= 2.5 km

so,

${2.5}^{2} - {0.7}^{2} = h {}^{2}$


$6.25 - 0.49 = h {}^{2}$



$5.76 = {h}^{2}$



$\sqrt{5.76} = h$


$2.4 = h$


$<b>So, height of the mountain=2.4 km</b>$

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Warm regards

@Laughterqueen

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