Given: The radius of a sphere = three times the radius of the base of a cylinder. The height of the cylinder = nine times the radius of its base. The total surface area of the cylinder = volume of the sphere Formula Used: The total surface area of the cylinder = 2πr(r + h) The volume of the sphere = (4/3)πr3 Calculation: Let the radius of the base of a cylinder be r. The radius of a sphere = 3r The height of the cylinder = 9r According to the question. The total surface area of the cylinder = Volume of the sphere ⇒ 2πr(r + h) = (4/3)πr3 ⇒ 2 × r(r + 9r) = (4/3) (3r)3 ⇒ 2 × 10r2 = (4/3) × 27r3 ⇒ 20/(4 × 9) = r ⇒ r = 5/9 So, the height of the cylinder = 9r = 9 × (5/9) = 5 unit. ∴ The height of the cylinder is 5 unit.