# The slant height

Let the radius of base be ‘r’ km and slant height be ‘l’ km

Slant height of conical mountain = 2.5 km

Area of its base = 1.54 km2

Area of base is given by πr2

πr2 = 1.54 km2

22/7 × r2 = 1.54 km2

r2 = 1.54 × 7/22 km2 = .49 km2

r = 0.7 km

Let ‘h’ be the height of the mountain

We know,

l2 = r2 + h2

Substituting the values of l and r in the above equation

2.52 = 0.72 + h2

h2 = 2.52 – 0.72 = 6.25 – 0.49 km2

h2 = 5.76 km2

h = 2.4 km

Height of the mountain = 2.4 km

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