Q. 75.0( 5 Votes )

# The area of the base of a right circular cone is 154 cm^{2}. If its slant height is 25 cm then find the height of the cone.

Answer :

Area of base of cone = 154 cm^{2}

Let r be the radius of cone

Area of base of cone = πr^{2}

⇒ πr^{2} = 154

⇒ × r^{2} = 154

⇒ r^{2} =

⇒ r^{2} = 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 = 7^{2} + h^{2}

⇒ 625 = 49 + h^{2}

⇒ h^{2} = 625 – 49

⇒ h^{2} = 576

⇒ h = ± 24

Height cannot be negative therefore h = 24 cm

Height of cone is 24 cm

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