Answer :

We have

Given: Curved surface area (CSA) = 251.2 cm^{2}

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,

AB^{2} = AO^{2} + OB^{2}

⇒ AO^{2} = AB^{2} – OB^{2}

⇒ h^{2} = 10^{2} – 8^{2}

⇒ h^{2} = 100 – 64

⇒ h = √36 = 6

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

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