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30 May, 11:15

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.

V=1/3 a^2h

Here, a is the side length of the pyramids square base and h is it's height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3+_x^2+_=0 can be used to find that the length of the sculptures base is _ centimeters.

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  1. 30 May, 11:17
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    side length of sculpture = 9 cm

    height of sculpture = 6cm

    Step-by-step explanation:

    Given that,

    volume of sculpture = 162cm³

    side length of sculpture = x

    height of sculpture = x-3

    formula for volume of sculpture

    V=1/3 a²h

    by putting values, the equation can be used to find the length of the sculpture's base

    162 = 1/3 (x) ² (x-3)

    162 (3) = (x) ² (x-3)

    486 = x² (x-3)

    486 = x³ - 3x²

    x³ - 3x² - 486 = 0

    x = 9 (using a graph tool / calculator equation mode)

    side length of sculpture = 9 cm

    height of sculpture = 9 - 3

    = 6cm
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