The area of the base of a cone is 314 cm² and the curved surface area…

Area of base = \(\pi \)r²

   ⇒ 314 = \(\pi \)r²

   ⇒ r = 10 cm                                (Take  \(\pi \) = 3.14)

C.S.A. = \(\pi \)rl

   ⇒  628 = 3.14 × 10 × l

   ⇒ l = 20 cm

h = \(\sqrt {l^2 - r^2}\) = \(\sqrt {400 - 100}\) = \(\sqrt {300}\) = 10\(\sqrt{3}\)

Volume = \(\frac{1}{3}\) \(\pi \)r²h

            = \(\frac{1}{3}\) × 3.14 × 100 × 10\(\sqrt{3}\) = \(\frac{3140\sqrt {3}}{3}\) cm³