Q7 of 67 Page 193

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.

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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