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Math Help - numercial reasoning

  1. #1
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    numercial reasoning

    A rectangular prism measures 6cm by 1cm 8cm. The prism is cut into cubes of 2cm.The number of such cubes will be:
    a)60
    b)48
    c)80
    d)64


    My teacher said it was A but i still dont understand y
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    I think something is wrong with the question you have given
    it should be
    6x10x8 and NOT 6x1x8(can you cut a cube of 2cm side from a prism of any of its dimension 1cm)
    -------------------------------------

    The best way here is check the volume

    Volume of prism = Total volume of all the prisms

    6x 10 x 8 = 480cm^3

    Volume of a single prism = 2x2x2 = 8cm^3

    Lets say we got n prisms , so

    8n = 480

    n = 60 cubes

    Thus we got 60 cubes
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  3. #3
    MHF Contributor

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    As ADARSH said, you can't just 'cut' a rectangle with one side of length 1 into cubes have all sides of length 2. The only way this problem makes sense is if we are allowed to "glue" pieces together. In that case, the number of cubes is just the volume of the prism divided by the volume of one cube.
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  4. #4
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    Hello, kl050196!

    I agree with ARDASH . . . the second dimension shoud be 10 cm.


    A rectangular prism measures 6 cm x 10 cm x 8 cm.
    The prism is cut into cubes of side 2cm.
    The number of such cubes will be:

    . . (a)\;60 \qquad(b)\;48\qquad (c)\;80\qquad(d)\;64

    The total volume is: . 6 \times 10 \times 8 \:=\:480\text{ cm}^3

    Each cube has a volume of: . 2^3 \:=\:8\text{ cm}^3

    There is enough material to make: . \frac{480}{8} \:=\:60\text{ cubes.}

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