Answer :

Given: Volume of cone (V) = 1212 cm^{3}

Height of cone (h) = 24 cm

We know the formula of volume of cone,

Volume = πr^{2}h /3

⇒ 3V = πr^{2}h

⇒ r^{2} =

⇒

⇒

⇒

⇒ r^{2} = 48.20 …(i)

⇒ r = √48.20 = 6.94

⇒ r ≈ 7 …(ii)

We know,

l = √(r^{2} + h^{2})

⇒ l = √(48.20 + 24^{2}) [from (i)]

⇒ l = √(48.20 + 576)

⇒ l = 24.98

⇒ l ≈ 25 …(iii)

⇒ Slant height of cone is 25 cm.

Curved surface area of cone is given by,

CSA = πrl

⇒ [from (ii) and (iii)]

⇒ CSA = 550 …(iv)

Thus, curved surface area of cone is 550 cm^{2}.

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