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.

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slant height of a conical mountain and its base values are given by using cone volume or area formula find the value of height of the mountain this question from RS Aggarwal book Exercise 17A and Page number 787

Given,

Slant height of conical mountain = 2.5 km

Area of its base = 1.54 km

^{2}Let the radius of base be ‘r’ km, height of the mountain is ‘h’ km and slant height be ‘l’ km

Area of base = πr

^{2}1.54 = πr

^{2}1.54 = 22/7 r

^{2}or r = 0.7 km

Using Pythagoras Theorem,

l

^{2}= r^{2}+ h^{2}(2.5)

^{2}= (0.7)^{2}+ h^{2}6.25 – 0.49 = h

^{2}or

h = 2.4 km

∴ height of the mountain is 2.4 km