A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown. What is the surface area of the figure? Express the answer in terms of π.

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