Question

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.

Answer 1

side length of sculpture = 9 cm

height of sculpture = 6cm

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