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7 December, 06:41

Some ice sculptures are made by filling a mold with water and then freezing it. A pyramid shaped mold has a height that is 1 foot greater than the length of each side of its square base. The volume of the ice sculpture is 4 cubic feet. What are the dimensions of the mold

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  1. 7 December, 07:03
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    The dimensions of the base of the mood is square, given by 2 ft by 2 ft

    And the height of the mood = 3 ft.

    Explanation:

    Volume of a pyramid = (1/3) (Area of base) (perpendicular height)

    Let the length of the square base be b

    Let the perpendicular height be h

    Area of base = b²

    Perpendicular height = h = b+1

    Volume of the pyramid = 4 ft³

    4 = (1/3) (b²) (b+1)

    12 = b² (b+1)

    b³ + b² = 12

    b³ + b² - 12 = 0

    Solving the polynomial,

    b = 2 ft or - 1.5 ft

    And since dimensions cannot be negative,

    b = 2 ft.

    The height of the mood = b + 1 = 3 ft
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