Q. 75.0( 5 Votes )

The area of the base of a right circular cone is 154 cm2. If its slant height is 25 cm then find the height of the cone.

Answer :

Area of base of cone = 154 cm2


Let r be the radius of cone


Area of base of cone = πr2


πr2 = 154


× r2 = 154


r2 =


r2 = 7 × 7


r = 7 cm


Slant height = 25 cm


Let h be the height of cone


Slant height =


25 =


Squaring both sides we get


625 = 72 + h2


625 = 49 + h2


h2 = 625 – 49


h2 = 576


h = ± 24


Height cannot be negative therefore h = 24 cm


Height of cone is 24 cm


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