The surface area of the figure is 96 + 64π ⇒ 1st answer Step-by-step explanation: * Lats revise how to find the surface area of the cylinder - The surface area = lateral area + 2 × area of one base - The lateral area = perimeter of the base × its height * Lets solve the problem - The figure is have cylinder - Its diameter = 8 cm ∴ Its radius = 8 ÷ 2 = 4 cm - Its height = 12 cm ∵ The perimeter of the semi-circle = πr ∴ The perimeter of the base = 4π cm ∵ The area of semi-circle = 1/2 πr² ∴ The area of the base = 1/2 × π × 4² = 8π cm² * Now lets find the surface area of the half-cylinder - SA = lateral area + 2 × area of one base + the rectangular face ∵ LA = perimeter of base × its height ∴ LA = 4π × 12 = 48π cm² ∵ The dimensions of the rectangular face are the diameter and the height of the cylinder ∴ The area of the rectangular face = 8 × 12 = 96 cm² ∵ The area of the two bases = 2 × 8π = 16π cm² ∴ SA = 48π + 16π + 96 = 64π + 96 cm² * The surface area of the figure is 96 + 64π
