Respuesta :
Let
x-----------> the side length of a pyramid square base
h-----------> the height of the sculpture in the shape of a pyramid
we know that
h=(x-3)
Volume=162 cm³
Volume=x² *(x-3)/3
then
x² *(x-3)/3=162----------> x³-3x²=486----------> x³-3x²-486=0
x³-3x²-486=0-------- this equation can be used to find the length of the sculpture’s base
using a graph tool-----------> to find the solution
x=9 cm -------------> see the attached figure
h=(x-3)-----> h=9-3--------> h=6 cm
the answer is
the length of the sculpture’s base is 9 cm
the height of the sculpture is 6 cm
x-----------> the side length of a pyramid square base
h-----------> the height of the sculpture in the shape of a pyramid
we know that
h=(x-3)
Volume=162 cm³
Volume=x² *(x-3)/3
then
x² *(x-3)/3=162----------> x³-3x²=486----------> x³-3x²-486=0
x³-3x²-486=0-------- this equation can be used to find the length of the sculpture’s base
using a graph tool-----------> to find the solution
x=9 cm -------------> see the attached figure
h=(x-3)-----> h=9-3--------> h=6 cm
the answer is
the length of the sculpture’s base is 9 cm
the height of the sculpture is 6 cm