# 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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