# A cone of slant height 25cm has a curved surface area of 550 cm2. find the height of the cone and its volume

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Slant Height(l) = 25 cm and Curved Surface area of cone =

Let Radius of cone be r and height be h

Curved Surface area of cone = rl =

r(25) =

r=

r = (550/22*25) *7 cm

r= 7 cm

Therefore radius of cone is 7 cm.

By pythagoras theorem, we have

=>

Therefor, Height of the cone is 24 cm

Volume of cone = 1/3h = 1/3 *22/7 *7 49 * 24

Volume = 1232