Answer:
The figure obtained is a cylinder
The exact surface area is 1440π.
Step-by-step explanation:
* Lets study the rotation of a rectangle around one of its sides
- If the dimensions of the rectangle are length (L) and width (W)
- If we rotate the rectangle around its length (L), we will construct
a cylinder with radius = W and height = L
- If we rotate the rectangle around its width (w), we will construct
a cylinder with radius = L and height = W
∵ The surface area of any cylinder =
perimeter of base × height + 2 base area
∵ The base is a circle
∴ perimeter base = 2πr and base area = πr²
∴ The surface area = 2πrh + 2πr²
* In first case:
- Surface area = 2π(W)L + 2π(w)² = 2πWL + 2πW²
* In second case:
- Surface area = 2π(L)W + 2π(L)² = 2πLW + 2πL²
* Now lats check our question:
∵ L = 22 and W = 18
- It will rotate around the largest side
∴ It will rotate around L
∴ The figure obtained is a cylinder
* From the explanation above this is the first case
∵ L = 22 and W = 18
∵ The surface area = 2πWL + 2πW²
∴ The surface area = 2 × 18 × 22 × π + 2 × (18)² × π
= 792π + 648π = 1440π
* The exact surface area is 1440π.
