Answer:
7 cubes (having 2 m sides) can be completely covered with 7500 ml of paint, assuming the "2m" refers to side length in the question.
Step-by-step explanation:
No definition of a "cube" is provided. The area in a cube must be known to determine the number of cubes that the paint will cover. The entry "2 m" is confusing. Is this supposed to be 2m^2, a unit of area for each cube? 2m is a length. If 2 m is the side of a cube, then the following calculation will work:
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1. Calculate the area of a cube:
A cube has 6 faces, all having the same lengths (2 m). The are of one face is the quare of the length, or 4 m^2. 6 faces make the total area 24 m^2 per cube.
This can be made into a conversion factor: (24 m^2/cube)
2. Calculate the area that 7500 ml of paint will cover:
Since 40ml of paint covers 1 m^2, we can write a conversion factor: (1 m^2)/(40 ml).
3. Calculate the number of cubes covered by 7500 ml of paint:
Use the conversion factors. Focus on arrange the factors so that the units cancel to just cubes, the desired answer.
a) Start with the 7500 ml and use a conversion factor to eliminate ml and leave on m^2. This will tell us how many square meters of surface the 7500 ml of paint will cover. The first conversion factior has both ml and m^2, so lets use it. The factor, as written, can be multiplied by the 7500ml to leave only m^2, since the ml units will cancel:
(7500 ml)*[(1 m^2)/(40 ml)] = 187.5 m^2
b) The desired final unit is simply cubes. The second coversion factor has both m^2 and cubes, so we can use it to convert m^2 into cubes. But note that if the conversion facotr is multiplied, we'll wind up with unit of m^4/cube:
(187.5 m^2)*[(24 m^2/cube) [The resulting unit of m^4/cube makes no sense]
In this situation, we may divide instead:
(187.5 m^2)/[(24 m^2/cube) = 7.81 cubes
[This step can be written as:
(187.5 m^2)/[(24 m^2/cube) is the same as [(187.5m^2/24)] (cube/m^2)
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II don't enjoy division, so my preferred step is o invert the conversion factor:
Original: (24 m^2/cube)
Inverted: (1 cube/24 m^2) This is allowed since in a conversion factor, both the top and bottom are equal. [So we can write (1 foot/12 inches), or (12 inches/1 foot), for example. Both are correct.]
Using this approach:
(187.5 m^2)*(1 cube/24 m^2) = 7.81 cubes The m^2 units cancel leaving only (187.5/24) cubes (or 7.81 cubes).
Since the question stipulates that the cubes must be "completely" covered, we need to round down. That make 7 cubes (having 2 m sides) can be completely covered with 7500 ml of paint.