## The length of a room is two times its breadth and breath is 2 times its height.if the volume of the room is 512 m*3.how much is the cost of

Question

The length of a room is two times its breadth and breath is 2 times its height.if the volume of the room is 512 m*3.how much is the cost of plastering the wall at 5.50 per m*2?

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7 months 2021-10-07T10:03:37+00:00 2 Answers 0 views 0

1. 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]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.