Question

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

Answer 1

Hope that this answer helps you.

Answer 2

Answer:

$Height\:of \:the \:cone(h) =2.4\:km$

Step-by-step explanation:

Dimensions of a Conical mountain:

Slant height (l) = 2.5 km

Base area (A)=1.54 square km

Let radius of the base= r km

$\pi r^{2}=1.54$

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

$\implies r^{2}=1.54 \times \frac{7}{22}\\=0.49$

$\implies r =\sqrt{0.49}$

$\implies r = 0.7 \:km$

$Now, \\Height\:of \:the \:cone(h) = \sqrt{l^{2}-r^{2}}\\=\sqrt{(2.5)^{2}-(0.7)^{2}}\\=\sqrt{6.25-0.49}\\=\sqrt{5.76}\\=2.4\:km$

Therefore,

$Height\:of \:the \:cone(h) =2.4\:km$

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