Answer :

Given: Curved surface area of cone (CSA) = 2200 cm^{2}

Slant height of cone (l) = 50 cm

For total surface area, we have the formula

TSA = πrl + πr^{2}

⇒ TSA = CSA + πr^{2} [∵, Curved surface area (CSA) = πrl] …(i)

Where, r = radius of the base of the cone

We have CSA, we just need to find radius of the base of the cone (r).

So, we know

CSA = πrl

Substituting values in above equation,

⇒

⇒

⇒ r = 14

⇒ Radius of the base of the cone = 14 cm

Thus, substituting value of CSA and r in equation (i),

⇒ TSA = 2200 + 616

⇒ TSA = 2816

Thus, total surface area of cone is 2816 cm^{2}.

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