The area of the base of a cone is 616 cm² and the curved surface area is 2200 cm². The volume of this cone will be:

9856  cm³

Area of base = \(\pi \)r² = 616

⇒ r² = \(\frac{616\;×\;7}{22}\) = 196

⇒ r = 14

CSA = \(\pi \)rl = 2200

⇒ l = \(\frac{2200\;×\;7}{22\;×\;14}\) = 50

⇒ l = 50

Using Pythagoras theorem. 

h = \(\sqrt {l^2 - r^2}\) = \(\sqrt {50^2 - 14^2}\) = 48

Now, Volume = \(\frac{1}{3}\) × \(\pi \)r²h = \(\frac{1}{3}\) × \(\frac{22}{7}\) × 196 × 48 =  9856 cm³