Question

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

Answer 1

Right circular cone

Solve for height

h≈2.49km

l Slant height

2.5

km

A Surface area

1.54

km²

Using the formulas

A=πrl+πr2

l=r2+h2

Solving forh

h=2πl2+2lπ(πl2+4A)﹣4A

2π=2·π·2.52+2·2.5·π·(π·2.52+4·1.54)﹣4·1.54

2·π≈2.49331km

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