Given: The height of the cylinder = half of the radius of the cylinder The volume of the cylinder = 539 cm3 Formula Used: The volume of the cylinder = πr2h The total surface area of the cylinder = 2πr(r + h) Where, r = Radius of the cylinder h = Height of the cylinder, π = 22/7 Calculation: Let the radius of the cylinder(r) be x cm. Then, the height of the cylinder(h) = (x/2) cm According to the question, πr2h = 539 ⇒ (22/7) × x2 × (x/2) = 539 ⇒ (11x3)/7 = 539 ⇒ x3 = 539 × (7/11) ⇒ x3 = 49 × 7 ⇒ x3 = 343 ⇒ x = 7 Hence, r = 7 cm h = (7/2) cm The total surface area of the cylinder = 2πr(r + h) ⇒ 2 × (22/7) × 7 × {7 + (7/2)} ⇒ 44 × (21/2) ⇒ 22 × 21 ⇒ 462 cm2 ∴ The total surface area of the cylinder will be 462 cm2.