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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Answer 1

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Answer 2

It will cost 2,464 currency for plastering 448
`m^(2)` of the wall.

Explanation:

Step 1:

The volume of this room is determined by multiplying its length, breadth, and height.

From the question;

`length=2(breadth), l = 2h,`

`breadth = 2(height), b = 2h,`

So
`length = 4h.`

Step 2:

The volume of the room
`= lbh = 512`,

Substituting the values of length and breadth in the above equation, we get

`(4h)(2h)(h) = 512, 8h^(3) = 512.`

`h^(3) = 64, h = 4.`

So
`l = 4h = 4(4) = 16, w = 2h = 2(4)=8.`

So l = 16 m, w = 8 m and h = 4 m.

Step 3:

If each
`m^(2)` 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
`1^(st)` set =
`(length) (width) = (16)(8) = 128 m^(2).`

Area of the
`2^(nd)` set =
`(length)(height) = (16)(4) = 64 m^(2).`

Area of the
`3^(rd)` set =
`(width)(height) = (8)(4) = 32 m^(2).`

The Surface area of these three sets = 128 + 64 + 32 = 224
`m^(2)`.

Since there are two sets,

The total surface area =
`224 (2) = 448 m^(2)`.

Step 4:

If each
`m^(2)` of the wall costs 5.50,

448
`m^(2)` costs;
`448(5.50) = 2,464` currency.