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9 February, 11:52

Roberto wants to build a wooden box with a volume of 8 cubic feet. How many different boxes, all with whole number dimensions and a different size base, will have a volume of 8 cubic feet?

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  1. 9 February, 12:17
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    Three different boxes will have a volume of 8 cubic feet

    Step-by-step explanation:

    The formula for the volume of box = Length, l * Breadth, b * Height, h

    Where, the base size = l * b

    The number of different boxes are;

    l * b * h

    1 * 1 * 8

    1 * 2 * 4

    2 * 4 * 1

    2 * 2 * 2

    1 * 8 * 1

    Whereby the base are to be different, we note that the following;

    1 * 8 * 1 = 1 * 1 * 8

    1 * 2 * 4 = 2 * 4 * 1

    Hence the different boxes with different bases that will have a volume of 8 ft³ are;

    h * b * l

    1) 1 * 1 * 8

    2) 1 * 2 * 4

    3) 2 * 2 * 2

    Which are three different boxes with dimensions;

    Box 1: Length = 8 ft, breadth = 1 ft., and height = 1 ft

    Box 2: Length = 4 ft, breadth = 2 ft., and height = 1 ft

    Box 3: Length = 2 ft, breadth = 2 ft., and height = 2 ft.
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