It will cost 2,464 currency for plastering 448[tex]m^{2}[/tex] of the wall.
Step-by-step explanation:
Step 1:
The volume of this room is determined by multiplying its length, breadth, and height.
From the question;
[tex]length=2(breadth), l = 2h,[/tex]
[tex]breadth = 2(height), b = 2h,[/tex]
So [tex]length = 4h.[/tex]
Step 2:
The volume of the room [tex]= lbh = 512[/tex],
Substituting the values of length and breadth in the above equation, we get
[tex](4h)(2h)(h) = 512, 8h^{3} = 512.[/tex]
[tex]h^{3} = 64, h = 4.[/tex]
So [tex]l = 4h = 4(4) = 16, w = 2h = 2(4)=8.[/tex]
So l = 16 m, w = 8 m and h = 4 m.
Step 3:
If each [tex]m^{2}[/tex] of the wall costs 5.50, we need to calculate the surface area of the room.
There are six sides of the room (2 sets of 3 sides)
Area of the [tex]1^{st}[/tex] set = [tex](length) (width) = (16)(8) = 128 m^{2}.[/tex]
Area of the [tex]2^{nd}[/tex] set = [tex](length)(height) = (16)(4) = 64 m^{2}.[/tex]
Area of the [tex]3^{rd}[/tex] set = [tex](width)(height) = (8)(4) = 32 m^{2}.[/tex]
The Surface area of these three sets = 128 + 64 + 32 = 224 [tex]m^{2}[/tex].
Since there are two sets,
The total surface area = [tex]224 (2) = 448 m^{2}[/tex].
Step 4:
If each [tex]m^{2}[/tex] of the wall costs 5.50,
448 [tex]m^{2}[/tex] costs; [tex]448(5.50) = 2,464[/tex] currency.
