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Let the radius and height of the cylinder ber cm and h cm respectively. Given, Total surface area of the cylinder = 462 cm2∴ 2pr (r + h) = 462 cm2 .. .(1)Lateral surface area of cylinder = 1/3 × Total surface area of cylinder (Given)∴ 2prh =1/3 × 462 = 154 cm2 ... (2) From (1) and (2), we have{2pr(r+h}/{2pr} = 462 cm2 / 154 cm2(r+h) / h = 3r = 3h-h=2hr = 2hFrom (2), we have2prh =154 cm2(2 x22rxr) /(7x2)}r = 7cmh = r/2=7/2=3.5cm ∴ Volume of the cylinder = pr2h =22x7x7/3.5=539 cm3