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^2hHere, 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.
Accepted Solution
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Answer:side length of sculpture = 9 cmheight of sculpture = 6cm Step-by-step explanation:Given that,volume of sculpture = 162cm³side length of sculpture = xheight of sculpture = x-3formula for volume of sculptureV=1/3 a²hby putting values, the equation can be used to find the length of the sculpture’s base162 = 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 cmheight of sculpture = 9 - 3 = 6cm