Question

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

Answer 1

$\text{Area of base } = 1.54 {km}^{2} \\ \pi {r}^{2} = 1.54 \\ {r}^{2} = \frac{1.54 \times 7}{22} \\ r = \sqrt{ \frac{1.4 \times 7}{22} } = 0.7km \\ \text{We know that,} \\ {l}^{2} = {r}^{2} + {h}^{2} \\ {h}^{2} = \sqrt{ {l}^{2} - {r}^{2} } \\ \: \: \: \: \: \: = \sqrt{ {2.5}^{2} - {0.7}^{2} } \\ \: \: \: \: \: \: = \sqrt{5.76} = 2.4km$
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