Answer:
The surface area = 120π units² ≅ 377 units²
The volume of the cylinder = 144π ≅ 452.4 units³
Explanation:
* When a rectangle is rotating around one of the axis, 360°
then, the formed figure is a cylinder withe height equal the
side which rotated over it and the radius is the other dimension
∵ RECT is rotated 360° about the y-axis
∴ It formed a cylinder with height = RE and radius = EC
- R = (0 , 3 , 6) , E = (0 , 7 , 6) , C = (0 , 3 , 0) , T = (0 , 7 , 0)
∴ The length of RE = 7 - 3 = 4 units ⇒ height of the cylinder
∴ The length of EC = 6 - 0 = 6 units ⇒ radius of the cylinder
* The surface area of the cylinder = lateral area + 2 × area of the base
∵ Lateral area = perimeter of the base × height
∵ The base is a circle with radius = 6 units
∴ The perimeter of the base = 2πr = 2π(6) = 12π units
∵ The length of the height is 4 units
∴ The lateral area = 12π × 4 = 48π units²
∴ The area of the base = πr² = π(6²) = 36π units²
∴ The surface area = 48π + 2 × 36π = 120π units² ≅ 377 units²
* The formula of the volume of the cylinder is area of the base × height
∵ Area of the base = 36π units²
∵ The height = 4 units
∴ The volume of the cylinder = 36π × 4 = 144π ≅ 452.4 units³