Q3 of 32 Page 119

Curved surface area of a cone is 251.2 cm2 and radius of its base is 8cm. Find its slant height and perpendicular height. (π = 3.14)

We have


Given: Curved surface area (CSA) = 251.2 cm2


Radius of the base of cone (r) = 8 cm


We know the formula of curved surface area of cone,


CSA = πrl


Where l = slant height of cone


⇒ 251.2 = 3.14 × 8 × l


⇒


⇒ l = 10


So, we have found slant height of cone (l) = 10 cm


Now, using Pythagoras theorem in ∆AOB,


AB2 = AO2 + OB2


⇒ AO2 = AB2 – OB2


⇒ h2 = 102 – 82


⇒ h2 = 100 – 64


⇒ h = √36 = 6


Thus, slant height of cone is 10 cm and height of cone is 6 cm.


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